implementation of a wetting and drying model in

IMPLEMENTATION OF A WETTING AND DRYING MODEL IN SIMULATING THE ANDROSCOGGIN/KENNEBEC PLUME AND THE CIRCULATION IN CASCO BAY By Yi Du B.S. Ocean University of China, 2002

A THESIS Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science (in Oceanography)

The Graduate School The University of Maine August, 2008

Advisory Committee: Huijie Xue, Professor of School of Marine Science, Advisor Neal Pettigrew, Professor of School of Marine Science Bryan Pearce, Professor of Civil Engineering

IMPLEMENTATION OF A WETTING AND DRYING MODEL IN SIMULATING THE ANDROSCOGGIN/KENNEBEC PLUME AND THE CIRCULATION IN CASCO BAY

By Yi Du Thesis Advisor: Dr. Huijie Xue

An Abstract of the Thesis Presented In Partial Fulfillment of the Requirements for the Degree of Master of Science (in Oceanography) August 2008

Casco Bay, located on the west Maine coast, is characterized by a complex series of peninsulas, numerous small islands, and some intertidal zones. Previous studies suggested that Casco Bay is a source region of toxic algal bloom and such events are closely related to variations of sea surface salinity (Keafer, 2005). The Androscoggin/Kennebec estuary is less than 20km to the east. Discharges from the two rivers combined reach ~ 1.3xl010 m3 annually and the resultant plume is a key factor that drives salinity variability in Casco Bay. A comprehensive coastal ocean model is used to simulate the Androscoggin/Kennebec plume and the circulation in Casco Bay from 2004 to 2005. The model results compare favorably with moored observations from GoMOOS buoy C and

ship survey data. Wind and tidal forcing determine the spread of the plume in the bay. A wetting and drying (WAD) scheme is adapted to enhance the model ability to solve the detail conditions in shallow areas. By comparing the run without WAD, significant differences are presented. It suggests that the WAD scheme enhances the mixing and entrainment processes near the estuary, which results in stronger tidal intrusion into the estuary and thicker plume near the estuary mouth.

ACKNOWLEDGEMENTS I would like to express my gratitude to many people who helped me to carry out my thesis project. I would like to thank my advisor Dr. Huijie Xue for her endless patience, constant support, and encouragement. She always made time to explain something to me, no matter how busy she was. Without her help I could not have finished this book. I would also like to thank Dr. Neal Pettigrew and Dr. Bryan Pearce for providing their time and knowledge when needed. A very special thanks to the technicians, research assistants, graduate students in Ocean Modeling Group where I finished my Master's thesis. I have learned so much from those hardworking and dedicated people. Thanks to Steve cousins, our incredibly smart computer technician for putting hours to helping me to design and maintain the model. Thanks to my Mother, she always believed in me and encouraged me to follow my dreams and goals in life. Thank you for your love and support. Also thank you to my landlord Dana Buzzell, for always helping me revise my writing.

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TABLE OF CONTENTS ACKNOWLEDGEMENTS

ii

LIST OF TABLES

v

LIST OF FIGURES

vi

CHAPTER 1. INTRODUCTION

1

CHAPTER 2. A NUMERICAL SIMULATION OF THE CIRCULATION IN CASCO BAY AND K-A RIVER ESTUARY

5

2.1. Model description

5

2.2. Model results

6

2.2.1. Comparison with the buoy data

6

2.2.2. Comparison with the cruise data

10

2.3. Factors influencing the river plume

13

2.3.1. Definition of the K-A river plume

14

2.3.2. River discharge

18

2.3.3. Winds

23

CHAPTER 3. IMPLEMENTATION OF A WAD SCHEME IN THE POM

28

3.1. Oey's WAD scheme

28

3.2. Modifications

29

iii

3.2.1. Dry depth

29

3.2.2. Bottom drag coefficient

30

3.2.3. WETMASK and the calculation of baroclinic model

32

3.3. Idealized experiments

34

3.3.1. 2D alongshore wind driven test

34

3.3.2. 3D experiment with tidal forcing

36

3.4. Conservation

38

CHAPTER 4. IMPLEMENTATION OF WAD IN THE CASCO BAY MODEL

40

4.1. Introduction

40

4.2. Comparisons between the model with and without the WAD

41

4.2.1. The wetting and drying processes

41

4.2.2. Tidal intrusion into the estuary

43

4.2.3. Thickness of the Plume

46

CHAPTER 5. SUMMARY

51

REFERENCES

53

BIOGRAPHY OF THE AUTHOR

56

IV

-smg—

——;

:

LIST OF TABLES

Table 1. Zero-lag correlation coefficients between length/depth of the plume and river discharge/wind based on the entire modeled time series from March 2004 to December 2005

v

21

LIST OF FIGURES

Figure 2.1. Model grid and topography

6

Figure 2.2. Comparison of salinity and temperature between the model results and the observation at GoMOOS Buoy C

8

Figure 2.3. Comparison of surface current speed between the model results and the observation at GoMOOS Buoy C

10

Figure 2.4. Comparison of salinity between the model results and the UNH cruise data in 2005

12

Figure 2.5. Alongshore and cross-shore sections designed to quantify the river plume

15

Figure 2.6. Surface extension of the plume

18

Figure 2.7. Monthly averaged SSS and velocity for year 2005

19

Figure 2.8. Linear regression between lateral extensions of the plume and Q

22

Figure 2.9. Vertical distribution of salinity at zero point and predicted hb

25

Figure 2.10. Wind from mid October to mid November in 2005

26

Figure 2.11. Surface salinity distribution during two wind events

27

Figure 3.1. Definitions of WAD states in Oey's scheme

28

Figure 3.2. Bottom drag coefficient (CBC) at different depths

31

Figure 3.3. Flow diagram of the WAD scheme

33

Figure 3.4. The unperturbed water depth of the 2D model experiment (y-z cross-section)

34

vi

Figure 3.5. Elevation in the first 2 days

35

Figure 3.6. Boundary and initial conditions for 3D expericment

36

Figure 3.7. Salinity and Temperature distribution at y-z cross-section within a tidal cycle

37

Figure 3.8. Salinity and Temperature distribution at y-z cross-section within four days

38

Figure 3.9. Integrated flow in/out through the lateral boundary and the difference

39

Figure 4.1. Topography and model grid for the Casco Bay model with the WAD

41

Figure 4.2. Surface salinity distribution and circulation pattern during spring tides

42

Figure 4.3. Comparison of surface salinity at the cross-shore transect from March to April, 2005

44

Figure 4.4. Comparison of vertical salinity distribution at cross-shore trans-section

46

Figure 4.5. Surface salinity distribution and surface currents of April 4l , 2005

47

Figure 4.6. Vertical distribution of salinity at alongshore and cross-shore trans-sections

49

Figure 4.7. Along channel velocity and salinity distribution in the estuary on April 4th, 2005, in three interval

50

vn

Chapter 1. Introduction Flows in estuaries, inlets and lagoons are often characterized by shallow depth of wide lateral extent. Movement of seawater is not only horizontal, but also up and down due to tides and winds. The land-sea interface moves back and forth accordingly due to ebbing and flooding of tides. Foreshore and seabed become submerged at high water levels and exposed at low water levels. These areas are frequently described as the intertidal zone. In coastal ocean models that have fixed boundaries, assumptions as a never negative water depth and a vertical wall boundary are generally imposed to prevent an overland propagation of the fluid. In this case, the Wetting and Drying (WAD) process is ignored. These simplified models can be applied to large water bodies in which the portion with the mean water depth less than the range of the vertical movement of water level is small compared to the whole domain. However, to simulate the circulation in bodies of coastal waters encompassing considerable areas where the mean water depth is less than the range of water level movement, a numerical procedure known as WAD that allows land cells to become water cells and vice versa plays an important role in determining the circulation. A number of approaches have been implemented into the coastal and storm surge models to simulate the wetting and drying phenomena since the 1970's. Generally, two categories of methods have been used during the last 30 years. The early one is the moving boundary method. Coastlines in this method change with time, and there are number of grid cells. Mendelsohn (2001) used a moving boundary method to simulate the marsh inundation effects in the Cooper River Estuary. In practice, coastal areas having

1

complex topography like Casco Bay may contain tens of segments of coastline associated with small islands. It is difficult for the moving boundary method to trace all these landwater boundary changes. The WAD point treatment method has a domain encompassing the largest possible wet areas. A domain wide search is performed at every time step to determine whether individual cells are wet or dry. This method tends to have a better accuracy. Ten methods of WAD were reviewed by Balzano (1998) and had been tested in a 2D shallow water model. The crucial items in determining the wet/dry status are an exchange depth calculated by water levels and a retention volume that represent the maximum water flux of each cell. Since the maximum water flux is sensitive to the bottom irregularity, retention volume should consider the topography as well to alleviate underestimation/overestimation. Moreover, exchange depth determined only by water levels at cell sides often leads to nonphysical high water levels. Including water levels at cell centers with proper weights could improve this condition. Three of the ten methods in Balzano (1998) can cope with the above problems and capable of long-term computations. Our model is based on the Princeton Ocean Model (POM) (Mellor, 2004). The standard POM is a 3D ocean circulation model with fixed land boundaries. Different WAD schemes have been implemented into this model in recent years. Xie et al. (2004) developed a mass-conserving scheme in POM and tested it in an idealized storm experiment. Uchiyama (2004) simulated the tidal currents in San Francisco Bay. Oey (2005) implemented a new scheme in POM and simulated 3D processes in Cook Inlet, Alaska (2006, 2007). Among all these schemes, Oey's is the only one that can solve baroclinic flow. Thus, this WAD scheme has been adapted in my work, and several

2

modifications have been implemented to make this scheme stable enough and suitable for long-term computations. Casco Bay, located on the western Maine coast, has a complex topography. Fresh water discharge from the Kennebec-Androscoggin (K-A) river intrudes into the Bay from time to time, which also carries nutrients into the region. Observations indicate that there is a strong correlation between the salinity and algal abundance and suggest the Casco Bay region as a source region for toxic algal bloom (Keafer, 2005). The circulation pattern and the freshwater transport is of fundamental importance in helping scientists further understand the coastal dynamics and ecological system in the K-A estuary and Casco Bay. Many papers have studied the characteristics of the river plume base on both observations and numerical model results (e.g., Horner-Devine, 2007, Fong, 2001, Hickey, 1998). Most river plumes including the K-A river plume are surface trapped. Yankovsky (1997) used a simplified theory to predict the spreading and vertical structure of the surface trapped plume due to river discharge. On the other hand, the orientation and the size of the plume bulge can be changed by winds, tides and ambient flow (Hickey, 2005). K-A Rivers and the plume have been used as an archetype to set up idealized models to discuss the structures of surface trapped river plumes (Hetland, 2005). It was speculated that maintaining a very shallow depth at the coast or including WAD could prevent the formation of a backward-propagating bulge at the estuary mouth. Observational data also suggests that alongshore winds play an important role in controlling the shape of the K-A river plume (e.g. Fong, 1998, Choi, 2006, Pinonew, 2005).

3

This thesis is aimed at understanding the formation, evolution, and seasonal variability of the K-A river plume and the circulation in the Casco Bay area. In Chapter 2, a highresolution numerical model is used to simulate the K-A plume and the circulation of Casco Bay. The model has been integrated from April 2004 to December 2005 with real time surface forcing and observed river discharge. The model-data comparison will be presented to evaluate the model performance. The major discharge events and basic physical processes that control the K-A plume will be discussed. In Chapter 3, Oey's WAD algorithm is reviewed and a modification of the WAD algorithm will be presented. Several idealized numerical tests show that the modified WAD algorithm in POM is robust and can be used in long term numerical simulations. In Chapter 4, the newly developed POM with WAD process is applied to the Casco Bay area. The model results are compared with the original model without WAD to investigate how the WAD process affects the K-A river plume and circulation of the Casco Bay area. Chapter 5 presents conclusions from this research.

4

Chapter 2. A Numerical Simulation of the Circulation in Casco Bay and K-A Estuary

2.1. Model description The ocean circulation model used in this study is the Princeton Ocean Model (POM) (Mellor, 2003). It is a 3D, fully nonlinear, free surface, finite difference ocean model with the 2nd order turbulence closure scheme of Mellor and Yamada (1982). It has been broadly used in coast ocean modeling. Recently, it has been adopted for the Gulf of Maine nowcast/forecast system as a component of the Gulf of Maine Ocean Observing System (GoMOOS). The detailed model configuration and the model parameters can be found in Xue et al (2005). However, the resolution of the GoMOOS nowcast/forecast system is too coarse (3~5 km) to be used to study the Casco Bay area. So we have developed a high-resolution model nested in the GoMOOS nowcast/forecast system to simulate the circulation and dynamical processes in Casco Bay. The model is baroclinic with horizontal resolution of about 300 m. The model domain covers both the K-A estuary and the adjacent Casco Bay. The model has 285 x 274 curvilinear grid points. The fine model grid resolves the shoreline relatively well (Figure 2.1). There are 21 vertical sigma levels with higher resolution near the surface and bottom. The model has east, west and south open boundaries where the momentum, temperature and salinity are derived from the GoMOOS nowcast/forecast system. Realtime observed wind at GoMOOS buoy C and a model predicted heat flux are used as the surface forcing. Daily-recorded river discharges for the K-A River are obtained from

5

USGS gauge stations near Auburn, ME (01059000) and North Sydney, ME (01048265), respectively. In order to guarantee CFL condition, which relates time steps to the fluid velocity, the internal time step is 2.5 seconds and the external time step is 60 seconds. We integrated the model from April 2004 to December 2005. The model calculated horizontal velocity, temperature, salinity and other results are saved every 3 hours.

Figure 2.1. Model grid and topography. The model grid includes 285x274 points with one in every 10 grids shown in the map. Red dots indicate the location of observations, both buoys and stations. 2.2 Model results 2.2.1. Comparison with the buoy data GoMOOS Buoy C is located between the entrance to the western Casco Bay and the Western Maine Coastal Current (WMCC) (see Figure 2.1). It is approximately 25 km southwest of the K-A estuary. Water depth at Buoy C is ~ 45 m. Surface (1 m) and

6

subsurface (20 m) salinity and temperature as well as the currents at 2 m are recorded hourly. Wind, air pressure, waves and other data are also been collected. Figure 2.2 shows the modeled and observed time series of salinity and temperature from April 2004 to December 2005. A 33-hour low pass filter was used to remove the tides. The model simulated the freshening events in both spring and winter and reproduced the salinity pulses of 5—10 days time scale. However, the modeled salinity was higher resulting from the higher salinity at the coastal boundaries imported from the GoMOOS nowcast/forecast system (Xue et al., 2005) and the magnitudes of the salinity pulses were smaller than the observed. It is obvious that surface salinity (lm) decreased in response to spring river discharge peaks, but showed large contrasts in these two years. Freshening in 2004 occurred from April to September and the salinity dropped down about 2 psu. In 2005, a much wetter summer and fall resulted in lower salinity through the end of the year. Also, the maximum decrease reached 7 psu (observed) in April 2005 because of a much stronger discharge peak (about 2.5 times the 2004). Salinity variation at 20m was much smaller compared to surface. Though not directly influenced by the river discharge (buoyant flow only existed in a thin layer of the upper water column), freshwater gradually mixed downward and decreased the salinity below the plume. The annual mean salinity (at buoy C) of 2005 is slightly lower ( 20 km) were excluded. These results suggest that at high river discharge when plume water spreads farther offshore, impacts from winds and coastal currents are strengthened. Under moderate wind events, we get better correlations between river discharge and extensions. It suggests that the dots far from the regression lines are possibly influenced by wind forcing.

2.3.3. Winds A surface-trapped river plume has strong and almost instantaneous response to winds. From Table 1, the downstream/upstream extension seems to be influenced by both alongshore and cross-shore wind. However, the total length (L1+L2) does not correlate with wind. An acceptable interpretation is that wind can change the orientation and the center of the freshwater bulge while the total alongshore length of the bulge near the freshwater source is determined by the discharge. Also Table 1 indicates the cross-shore length of the plume is affected more by Ekman transport which is induced by the alongshore wind. Generally, northeasterly winds (downwelling favorable) and onshore winds limit the cross-shore extent, and conversely, southwesterly winds (upwelling favorable) and offshore winds help cross-shore spreading of the plume. Note that the wind effect is determined by not only their directions but also the magnitude and the duration as suggested by the integral Ekman parameter —— dt. J phf When moderate wind changes its direction all the time as in our complex model setting, the plume may not be able to respond quickly. Moreover, in the model, the time that it

23

takes for the freshwater outflow from the estuary mouth to reach the front is hard to determine. Thus, only particular events like storms or continuously upwelling favorable winds can be discerned from the modeled results. Within the plume water, salinity gradients in the vertical are much greater than the horizontal gradients at the surface. As pointed out by Hickey (1998), the maximum observed lateral gradient in the Columbia River plume is ~ 1 psu/km while the mean vertical salinity gradient within the plume water is on the order of 0.25 psu/m. If the gradient were used as the criterion in the vertical, the estimated plume thickness would have discrete jumps from one sigma level to another. Instead, we use the isohaline that has the averaged salinity of SI, S2, and S3 to calculate the thickness of the plume, h, which is shown as the red dotted line in the lower panel of Figure 2.9. An estimated thickness of the plume using a linear relationship between the equilibrium depth and Q° 5 is plotted as the white dotted line. The basic trend and main discharged events of the modeled structure coincide with our calculated h, though several deviations are observed. The biggest deviations are found during the high discharge periods. Although winds during the flooding time were not the strongest, their effects reached the maximum.

24

alongshore wind stress(N/m )

cross-shore wind stress(N/m ) -|QLI

I

I

1

I

J

I

I

1

I

J-

1

I

L

1

-I

1

1

1

salinity @ eatuary mouth

10

15

20

25

30

Figure 2.9. Vertical distribution of salinity at zero point and predicted hb. Upper panel: cross-shore wind stress; middle panel: alongshore wind stress; lower panel: vertical distribution of salinity at point O (see Figure 2.5), the predicted hb (white line) and the plume thickness (red line). Taking the spring freshet in 2005 as an example (April to June), there were four small discharge peaks during this period. The first peak was the biggest one and the peaks thereafter were getting smaller and smaller. However, the width of the alongshore plume during this period increased. At that time, a large region was covered by the plume water. The total buoyancy effect enhance the plume was remarkable due to the huge volume. During the first discharge peak in early April, onshore winds significantly constrained the spreading of the plume and deepened the plume. When the 2nd discharge peak arrived in May 2005, the plume water occupied the entire water column under the control of the downwelling favorable wind. From late April to early September in both years, dominant direction of the cross-shore wind was onshore. Wind continuously drove the plume close

25

to shore and increased the thickness of the river plume. Since the magnitude of the crossshore wind and the magnitude of the alongshore wind were comparable (3.05m/s for alongshore, 3.03m/s for cross-shore), during these periods the cross-shore wind tended to have a higher ability to spread or retain a downward transport. In the absence of the buoyancy forcing, the effect of strong winds can also be observed, not only in the plume region, but also on the whole domain. Figure 2.10 and 2.11 illustrate two wind events in October and November 2004. Under a downwelling favorable wind event (left panel in Figure 2.11, October 22), the plume was elongated in downstream direction but constrained along the coastline. During an upwelling favorable wind event (right panel in Figure 2.11), the direction of the plume was offshore and upstream, indicating that the upstream transport driven by the wind overwhelms the rotation effect during this time. Also, salty water rose from the subsurface to compensate the wind-induced offshore movement of the surface water.

Wind Stress (N/m 2 ) 1

1

1

1

1

1

1

'

1

/ft

1

1

1

1

1

1

1

1

1

1

1 | I

1

1

1

1

1

1

1

1

!

i

i

i

i

i

i

i

i

i

i

i

i

TV/'

1

1

i

16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 1011 12131415 October,2004 November2004

Figure 2.10. Wind from mid October to mid November in 2005. Two red lines highlight the downwelling and upwelling events shown in Figure. 2.11)

26

44.1

43.9-

43.9

43.7

43.7

43.5

43.5

43.3

43;

69.3

a) Figure 2.11. Surface salinity distribution during two wind events, a): downwelling favorable wind; b): up welling favorable wind.

27

Chapter 3. Implementation of a WAD Scheme in the POM Large tides may produce a sizeable intertidal zone in near shore environments. A model with WAD scheme enhances its ability to solve the detail conditions in these shallow areas. Including the WAD process in the model is expected to increase the physical realism of a simulation of hydrodynamic conditions. As well, the inclusion of WAD is also important for more accurate estimates of shoreline impacts by spilled oil or other chemicals. The original POM code does not include WAD. Recently, Oey (2005) developed a WAD algorithm embedded in POM, which can deal with intertidal zones and solve for the 3D baroclinic solution.

3.1. Oey's WAD scheme In Oey's WAD scheme (Oey, 2005), a minimum depth (drydep = 5 cm) was defined to determine the "dry" or "wet" state of each cell. He also introduced a group of masks for numerical convenience. When the total depth (D), which is the summation of water depth (H) and elevation (n), falls below the minimum depth, cells are considered as dry (Figure 3.1). As C-grid is the grid arrangement of POM, elevation and water depth is in the center of each cell, while velocities are specified at the cell's interface. Thus, on the C-grid, the "dry" or "wet" condition for velocity should be imposed at the interface. In addition, because of the shallow depth at the wetting and drying interface, the velocity profile across the interface to a dry cell is assumed purely barotropic in order to eliminate strong shears.

28

f

ALB HPC

\w X^/-^

Hsi^i&xed

«I

It*i*

\ f H*«

^W$

% CM

^^^4*^ ^sssa,.

Figure 3.1 Definitions of WAD states in Oey's scheme: wet when blue curve is above the orange curve; dry when orange curve is exposed (adapted from Oey, 2005). 3.2. Modifications 3.2.1. Dry depth Based on the Oey's scheme, we have introduced several modifications. To avoid numerical problems, we still choose a dry depth of 5 cm as a minimum depth to calculate the velocity even when the total water depth drops below this threshold. That is, when calculating velocity from the flux at cell sides, 5cm is set as the lower limit. However, the elevation is recalled for the next time step computation instead of the specified 5 cm, which is usually used in the thin layer technique (Oey, 2005). This modification ensures the conservation of water mass. Though in large coastal areas where the small change of mass does not significantly influence model results, in some shallow inlets, this artificial increase in volume can reduce the area of the intertidal zone considerably. Although we use water depth to check the status of each cell, additional treatment is needed to solve the velocity at the wet-dry interfaces. Masks (DUM, DVM) used to identify the existence of velocities do not determine the directions. Oey (2005) designed an adjustment that no water can flow from dry cells to wet cells to prevent anomalous outflow. A similar restriction is added in our scheme to allow only the flow from wet 29

cells to adjacent dry cells. With all these conditions, WAD is totally controlled by water mass flux in/out at each cell.

3.2.2. Bottom drag coefficient Another modification is at the bottom boundary. Bottom stress is determined by overlaying velocity and the bottom drag coefficient (CBC). In most ocean models, including POM, CBC is given as equation (3.1) by matching the near-bottom velocity to the "Law of the Wall":

CBC1 = MAX

K

,0.0025

Mzz(kbml)-z{kb)xd)f

(3.1)

ZOB where ZOB is the roughness parameter, K =0.4 the von Karman constant, and {zzikbmX) - z(kb)) x d the distance between the bottom and its nearest velocity grid point. The lower limit value of 0.0025 is assigned for deep water where the bottom layer is not resolved by the model. This original formula is applicable for water depth ranging from tens to thousands of meters. T1,

II

zz(kbm\) — z(kb) .. , , „ , . ., , *—- x a is less than 1, the negative logarithm value might cause ZOB

numerical problems. Mellor (2002) suggested a modified formula (Equation(3.2)) to avoid instability:

CBC2 = MAX

K1

,0.0025

m+zZ(kbml)-Z(kb)xd)f

ZOB

30

(3.2)

This redefined formula ensures positive values for the logarithmic term and was used in Oey's scheme. Based on the configuration of our model (22 sigma levels), the new formula does improve the adaptation in shallow flows (Figure 3.2, from 2 to 4 m). But in a very shallow water, for example, when water depth drops below 1.5 meters (which could happen frequently with the WAD), equation (3.2) still results in a bottom drag coefficient greater than 1.0. In the two formulas above, the roughness parameter ZOB (=0.01) is a constant. Here, we introduce a new function of ZOB and apply it to equation (3.1) to satisfy both shallow and deep water regions as: ZOB = 0.01x(l-eAxd)

(3.3)

where parameter A is determined by different model settings. In our model, A=-0.25.

Figure 3.2. Bottom drag coefficient (CBC) at different depths. Blue line uses the original CBC formula (eqn. 3.1) with a constant ZOB value (0.01). Red line uses the new CBC formula (eqn. 3.2) with a constant ZOB value (0.01). Magenta line uses the original CBC formula (eqn. 3.1) and the new ZOB function (eqn. 3.3).

31

In deep water, ZOB is very close to 0.01. The three bottom drag coefficient curves are almost identical when the depth is greater than 13 meters. The new roughness parameter represents a good numerical strategy that the CBC value is never larger than 1.0 in shallow water while matches the original curve in deep water.

3.2.3. WETMASK and the calculation ofbaroclinic mode When Oey (2005) simulated the WAD process, only the barotropic flow was defined at the wet-dry interface so that a uniform velocity profile was assigned to the internal velocity. The last WETMASK from the external loop was chosen as the WETMASK in calculating the internal mode. This may not be the best approximation since a cell can switch between wet and dry during the course of an internal loop. First, we introduce three new time-dependent masks for the internal model (WETMASKT, DUMT, DVMT) and use averaged quantities (ET, UTB, VTB, UTF, VTF) to recheck the WAD process for the internal mode. In addition, at the cells where the total depth (H+ n) is less than drydep (we regard it as dry cells), we use averaged temperature and salinity at each cell to make this thin water column have a vertically homogenous distribution. By doing this, we can both reduce numerical oscillations at the land-sea boundary and ensure that the heat and salt within the model domain are always conserved (see discussion below). A flow diagram of our modified WAD scheme is showed in Figure 3.3.

32

33

Figure 3.3 Flow diagram of the WAD scheme

3.3. Idealized experiments In order to test the modified WAD scheme and check its accuracy when implemented in POM, a 2D wind forced experiment and a fully 3D thermodynamic tidal mixing experiment are conducted.

3.3.1. 2D alongshore wind-driven test A basin with a sloping seabed is selected for the 2D WAD experiment (Figure 3.4). A small water pool and a topographic bump are added at its shallow part and that is the place we are most interested in (where the WAD takes place). Grid size varies from 1 km in deep waters to 40 meters in the shallow part to ensure adequate resolution for WAD processes.

11 i

i '•*

1 it*

a v*

1 :«»

1 i't

:»«

Figure 3.4. The unperturbed water depth of the 2D model experiment (y-z cross-section). The enlarged shallow part contains a small water pool (cm in depth) and a small topographic bump ( cm in height). All initial conditions are set to zero. A sinusoidal wind stress with a period of one day is uniformly specified over the domain: T(t) = W0sin(oX)

(3.4)

34

where oo=27i cpd, WG is the maximum wind stress. Strong alongshore wind would generate both up welling and downwelling events. We divide the 2-day simulation into four panels by time (Figure 3.5). Different colors indicate elevations at different hours. During the first 12 hours, as shown in the upper left panel, the wind direction is out of the paper, a decrease of elevation happens due to offshore Ekman transport. When the direction of wind is into the paper, onshore Ekman transport pushes water landward (right panels). Because of friction, during the drying process water level becomes concave, and during the wetting process water level convex. When the water is moving offshore, some water is retained in the water pool. As the wind blows, the water in the pool oscillates with wind and some of it can even spill out of the pool. When wind pushes water back to shore, the water pool immediately submerges under the water. As the water level continues to rise, water runs around the bump until the water level is high enough to submerge the whole bump.

wind 0

Ekman transport *

N-

0.5

0 -05

-1 -1.5

20

40

GO

SD

100

120

Figure 3.5. Elevation in the first 2 days. The stars indicate the elevation, and the green arrows represent the increase/decrease trend of elevation within every 12 hours.

35

3.3.2. 3D experiment with tidal forcing Next, we consider a hyperbolic tangent topography with flat bottom at its southern part (Figure 3.6). The horizental resolution of the model is 200 meters. At the southern boundary, a tidal signal with an amplitude of 8 meters and a half-day period is imposed. Initially, the land-sea interface is 70 km away from its southern boundary and both the temperature and salinity are linearly stratified (Fig. 3.6). EL @ Southern Boundary 10

Figure 3.6. Boundary and initial conditions for 3D expericment. Upper panel: the tidal signal enforced at the southern boundary. Middle panel: the initial salinity at y-z crosssection. Lower panel: the initial temperature distribution at y-z cross-section. WAD process happens within the area enclosed by magenta dashed lines and the model results of this area are showed in Figure 3.7 and 3.8. We run this model for 4 days under this strong tidal mixing condition. Figure 3.7 shows the vertical structures of salinity and temperature at high water level and low water level, respectively. Obviously, our WAD model is capable of describing the elevation

36

changes properly at a magnitude of 8 m. Because of the friction, when tide reaches its maximun at the southern boundary and begins to decrease (after 3 hours), water at the northern corner is sill moving upward and carrying the cold salty water from below. Contrarily, at low tide (after 9 hours), surface fresh warm water penetrates into depth. Vetical shears are first observed in the bottom boundary layer, which tends to be an onset of vertical mixing. It seems that strong mixing are constrained in a 10 meter layer near the bottom and most of the mixed waters propagate in the onshore direction. By comparing between the results after one day and four days (Figure 3.8 ), the temperauture and salinity structures do not change significantly offshore. The mixing processes only affect 10 to 15 km nearshore where the water depths are less than 20 meters. Although well mixed waters could be identified in shallow areas after several tidal cycles, the water colume offshore is still stratified as horizontal advection appears to outcompete the mixing. Salinity- after 3 hours

Salinity- after 9 hours

Figure 3.7. Salinity and temperature distributions at y-z cross-section within a tidal cycle. a)salinity after 3 hours; b)salinity after 9 hours; c) temperature after 3hours; d) temperature after 9 hours.

37

Salinity-after 96 hours

Sainity- after 24 hours

-—-7-~~~~~-

50

50

55

;)

60

65 (KM)

70

75

8(

55

60

65

70

75

60

50

d)

Figure 3.8. Salinity and temperature distributions at y-z cross-section within 4 days. a)salinity after 1 day; b)salinity after 4 days; c) temperature after 1 day; d) temperature after 4 days. 3.4. Conservation The model has been run continuously for a month with water flowing in/out at the boundary all the time to test the stability and conservation of the WAD scheme. The configuration of this test is the same as the previous 3D run. The integrated amounts of water flowing in/out match well with the increase/decrease of the volume within the whole domain. This demonstrates that the fluctuation of the water volume comes only from its lateral boundary and that the model itself does not create extra volume. The temperature and the salinity have similar performance as the water volume, as shown in Figure 3.9. The differences about 1% of the total value are caused by numerical instability. Thus, this modified WAD scheme has a desirable ability to conserve the mass and heat/salt with a favorable robustness.

38

Figure 3.9. Integrated flow in/out through the lateral boundary (blue curve) and the difference (=total value-integrated flow/out-initial value). The upper panel is the water volume, middle panel is the heat (needs to be multiplied by Cp), and lower panel is the salt.

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Chapter 4. Implementation of the WAD in the Casco Bay Model 4.1. Introduction Instantaneous flow in Casco Bay is largely influenced by semidiurnal tides. When tidal currents move around in the bay where the water depth is shallow and the bathymetry is complex with lots of islands and some intertidal zone (Figure 4.1), the circulation inside the bay is highly disturbed by the topography. Since the intertidal flats account for a sizeable percentage of the surface area at low water level, it is necessary to include the WAD processes in numerical models to increase the physical realism of the simulation. As well, flooding processes happening in the estuary can affect the formation of the river plume. As K-A river plume not only helps to deliver freshwater to its nearby region but also feeds the Western Maine Coastal Current (WMCC), the influence of WAD is not restricted to shallow areas. A model with the WAD scheme may help to resolve more details of water exchanges, which the model without the WAD may not be able to handle appropriately. Finally, the inclusion of WAD is important for more accurate estimates of shoreline that would be impacted by spilled oil or other chemicals. In order to simulate the WAD processes, a newly developed WAD scheme is implemented in the POM and applied to the K-A estuary and Casco Bay. Figure 4.1 is the topography used in the WAD case. As a reference, the same model is also run without the WAD. The purpose of this study is not to validate the simulation of intertidal zones, which would require a detailed database of shorelines. Instead, our goal is to determine the feasibility of applying the WAD for long-term simulations of the circulation in Casco Bay and the K-A estuary and to demonstrate the modifications to coastal processes when considering WAD of shallow areas.

40

Figure 4.1. Topography and model grid (285*274, every 10 grids are showed in the map) for the Casco Bay model with the WAD. The magenta dots represent the potential wet and dry areas. Red line in the map indicates the cross-shore transect shown in Figure 4.3. 4.2 Comparisons between the model with and without the WAD 4.2.1. The wetting and drying processes The M2 tide is the predominant tidal constituent in the Casco Bay region (Greenberg, 1984). From the historical data at the water level station in Portland, ME (NOAA/NOS, Station ID: 8418150), the tidal range in the Casco Bay region is about 4 meters, which creates 11582 acres of tidal flats and 500 acres of rocky shores around Casco Bay (Casco Bay Plan, 1995). By implementing a WAD algorithm into our model, flooding and ebbing processes within this region are simulated.

41

20050309 SSSiU at 15 hour 0 n*i

20050309 SSS&U si 21 hoc 50 :«n

Figure 4.2. Surface salinity distribution and circulation pattern during spring tides (March 9th, 2005).a) the model results with the WAD scheme at the highest water level; b) the model results without the WAD scheme at the highest water level; c) the model results with the WAD scheme at the lowest water level; d) the model results without the WAD scheme at the lowest water level;. Solid black lines are permanent coastlines. White dotes enclosed by these lines in the WAD experiment represent the intertidal zones. Figure 4.2 shows the comparison of surface salinity and velocity between the ggmodels with and without the WAD. The simulation presented here is during the spring tide (March 9, 2005). In order to highlight the ability to simulate wetting and drying processes, two particular times of that day were chosen: at the highest water level around 3:00 pm and at the lowest water level around 9:30 pm At the highest water level, the intertidal zones are flooded. The surface salinity in the inner Casco Bay and plume waters tends to be fresher without implementing the WAD. Currents in coastal areas are mainly in the offshore direction in both models with

42

and without the WAD. Distortions are observed in shallow areas like Casco Bay and regions near the K-A estuary when the wet/dry conditions in these areas change possible pathways. A notable new characteristics simulated by the model with the WAD is the salt-water intrusion into the estuary. During flooding period, the coastal water is pumped into the estuary and forms a several kilometer long salt-water intrusion. But in the simulation without the WAD, the freshwater flows all the way out of the estuary even during the flood tide. At low tide, most shallow regions in Casco Bay and K-A estuary are exposed and small tide pools and intertidal zone can be identified in Casco Bay. Especially in the inner Casco Bay, intertidal zones sheltered by small islands can form tidal flats that are linked along the coastlines. Also, numerous islands, which are probably submerged during flood, appear in Casco Bay region at low tide. Some islands are divided into smaller ones (e.g., Great Diamond Island & Little Diamond Island) at high water level while they connect with each other during low tide. In addition, the freshwater plume becomes smaller and more circular at the surface after using the WAD.

4.2.2. Tidal intrusion into the estuary Since the WAD scheme modulates the water depth caused by rising and falling tides, stronger influence of tides is expected. Figure 4.3 illustrates the back and forth movement of plume water in the cross-shore direction in the spring 2005 (March and April) in the two different model settings. In year 2005, river discharge in March was relatively low but followed by a strongest freshet in early April. The coastal part of the transect presented here is right outside the estuary mouth and extended offshore as seen

43

in Figure 4.1. We also include a part of the estuary in this transect to help fully trace the pathway of the plume front. The estuarine part of this transect follows the main channel of the estuary for about 30 km. A clearly semidiurnal tidal signal can be found from both model results. Events like huge river discharge and strong winds could modify this basic pattern. But two models respond quite differently to these events.

I

J .201 *

I

1 March 2005

'

• - •••-•••:

• •'"•J

' April 2005

Figure 4.3. Comparison of surface salinity at the cross-shore transect from March to April, 2005. (a): modeled surface salinity with WAD, zero points indicate the statistic center O (Fig. 2.6); (b): modeled surface salinity distribution without WAD; (c): modeled elevation at statistic center O; (d) river discharge; and (e) alongshore (blue line) and cross-shore wind (black line). 44

In the model without the WAD, the two river discharge peak events almost destroyed the tidal pattern. A consistent seaward plume formed during the high discharge events (April 4th~7th, 24th~30th) and the coastal seawater did not flow into the estuary channel even during the flood periods. Other events that might weaken the tidal pattern were the persistent upwelling/downwelling favorable wind. Both upwelling favorable wind events in March lasted for 5-10 days and helped transport freshwater offshore. The offshore salinity at surface dropped about 5 psu and the freshwater almost occupied the surface of this entire transect. The model with WAD allows stronger tidal intrusion. Coastal seawater (-30 psu) sometimes intruded more than 15 kilometers upstream into the estuary. It is interesting that the rhythm of this excursion in this run matched well with the spring-neap tidal cycles seen in Figure 4.3c. This tidal rhythm was much more pronounced and stable compared with the results from the model without WAD. Intensified seaward extensions were also observed in the model with WAD during the freshet events and the salty water intrusion seemed to be impeded by out rushing freshwater. However, the movement of seawater was still back and forth in the estuary channel and the phenomenon of salty water intrusion was clearly visible even during the peak discharge events. Figure 4.4 shows the vertical distribution of salinity at the transect. Estuary mouth is located about 35 kilometers away from the southern boundary of the model. The seaward excursion is about 5 kilometers in both model runs. In the case without WAD (lower panel), freshwater tilted over the salty waters and accumulated more at the surface, the surface freshwater can spread farther offshore than that in the case with the WAD. As already revealed in Figure 4.2, with the incoming tidal flows, the estuary

45

becomes wider and more coastal water is pumped into the estuary in the WAD case. Also, the WAD scheme enhances the mixing processes at the estuary and weakens the stratification. iawtaeaoiM &t «*» a n&i

sswaas»*3» »««- m n^

Figure 4.4. Comparison of vertical salinity distribution at cross-shore trans-section, a) without WAD (flooding); b) with the WAD (flooding); c) without WAD (ebbing); d) with the WAD (ebbing). 4.2.3. Thickness of the Plume The WAD process not only influences the tidal current and water property in the estuary, but also changes the formation and evolution of the river plume. Spreading of the river plume is determined by density anomaly and inflow velocity (Yankovsky, 1997). However, the width and orientation of the river mouth are also important. Stronger mixing observed in the WAD case reduces the density anomaly around the estuary mouth, thus the baroclinic balance between freshwater and coastal waters becomes

46

somewhat weaker and the radius of the river plume shrinks. In the two simulations, although the general behavior of the plume is usually quite consistent, differences can be distinguished. For example, the plume in the WAD case almost disappears during flood tide, and during ebbing the most obvious differences are the size and direction of the K-A plume (see Figure 4.2). Figure 4.5 shows the K-A plume developed after the highest river discharge event on April 4th, 2005. The surface area of the plume simulated without the WAD was almost twice that of the one simulated with the WAD. Without WAD, river water flowed out from the estuary mouth and formed the plume. The plume had a semi circular shape, which was centered at the mouth with a radius of ~ 25 km. Freshwater extended almost equally in all directions and formed a big isentropic bulge. No salty water was entrained into the plume at the surface. Large amount of fresh water spread into Casco Bay and mixed with salty water, which reduced the SSS to ~ 29 psu in Casco Bay. 20050404 M 24 tww 0 mtn

20050404 al 24 h