8lmer.marsci.uga.edu/tomales_data/Thesis/chapter7.doc · Web viewIn order to conserve the steep vertical gradients without the generation of spurious oscillations, the solution method

3D modelling of density current intrusions in Tomales Bay

7 THREE DIMENSIONAL (3D) MODELLING OF DENSITY CURRENT INTRUSIONS IN TOMALES BAY

The understanding of an estuary should incorporate and link physical processes

(including circulation and sediment transport), biogeochemical processes and

ecological studies. The difficulty in using estuarine classification schemes to

understand estuarine processes is that they are static and tend to focus on a particular

aspect of the system while ignoring others i.e. tidal forcing, river inflow. Jay, Geyer

and Montgomery (2000) developed a process-based geomorphic classification scheme

that highlighted the importance of determining the temporally varying residence time

but even improved classification methods still posses many limitations. A fuller

appreciation of estuarine character and function can be obtained from 3D modelling

of the coupled systems. 3D modelling is challenging in that reliable bathymetric,

water level and physical data is required to correctly simulate the hydrodynamics and

other processes within the system. However, if the data exists, modelling becomes a

valuable tool in understanding the system and its functioning.

A 3D model, the Princeton Ocean Model (POM) (Blumberg and Mellor, 1987;

Mellor and Yamada, 1982), was applied to Tomales Bay and successfully reproduced

the observed seasonal patterns in temperature and salinity (Robson, 1999). POM is a

three-dimensional, free-surface model that uses a sigma co-ordinate grid and the level

2.5 Mellor-Yamada turbulence closure scheme (Mellor and Yamada, 1982 cited in

Robson 1999). Vertical resolution is solved using a finite differencing scheme and

the Smagorinsky diffusivity is used for horizontal diffusion. POM does not include a

wetting and drying algorithm thus restricting the mean water depth in any cell to be

greater than or equal to the tidal amplitude in that cell (Robson, 1999).

Observations of the summer cold, upwelled water intrusions have not fully

contributed to answering the second part of the key questions posed in chapter 1 i.e.

the development and progression of cold ocean-water intrusions into the estuary under

varying conditions. However, to study the intrusions of upwelled water into the

estuary, a much more detailed configuration is required than that which had

previously been used (time scale of days as opposed to months). In this study, the

Delft3D model was applied to Tomales Bay in order to simulate cold-water intrusion

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events and to thus resolve the sensitivity to input parameters, answering the second

part of the key research questions. The advantages of using the Delft3D model are:

Delft3D incorporates a wetting and drying algorithm into the model,

Although the turbulence closure scheme needs to be specified, there is a choice of

4 different schemes,

Horizontal diffusivity values are specified by the user,

Forester filters are available as a method to inhibit artificial mixing both vertically

and horizontally,

A Thatcher-Harleman condition allows for the possibility that some of the water

that leaves the estuary on the ebb tide may re-enter the estuary with the following

flood tide and

The bottom friction can be specified as variable along the estuary.

Context of modelling in Tomales Bay

For an analysis that would provide full details of the estuarine circulation, a

comprehensive physical data set is required, including

Simultaneous water levels offshore and at different locations within the system

(tidal amplitudes and phases),

Detailed bathymetry,

Accurate physical data: temperature and salinity (at the offshore boundary and

within the system), measured at the same time as the water levels

Accurate current and fresh water discharge data, measured at the same time as the

water levels

Fluxes at the air-sea interface i.e. momentum fluxes due to winds, heat fluxes due

to insolation, sensible and latent heat fluxes and moisture fluxes due to

evaporation,

Knowledge of the sediments throughout the length of the system to estimate

roughness parameters and

Two independent data sets for calibration and verification (van Ballegooyen and

Taljaard, 2001).

The modelling performed in Tomales Bay was a more limited analysis, as a

comprehensive data set in order to fully model the estuarine circulation was not

available. The data collected in Tomales Bay was limited with regard to the driving

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parameters (water level and physical data) to calibrate and validate the model. The

modelling was thus aimed at determining both the capability of the model to

reproduce the cold ocean-water intrusion events, the response (development and

progression) of these intrusions to differing physical scenarios and the comparative

importance of the parameters to the intrusions.

The data available for the implementation of the Delft3D in Tomales Bay are

listed below:

Water levels - only had submerged pressure sensor data at station 12. No other in

situ water level data was collected. Offshore data was taken from water levels

collected at Bodega Marine Laboratory, 11 km away.

Bathymetry - downloaded N.O.A.A. and digitised bathymetry were converted to

MSL. The bathymetry was sufficient to resolve the required detailed features.

Temperature/salinity offshore - no measured data was available so data was taken

from temperature and salinity recordings measured at Bodega Marine Laboratory.

Initial conditions - the initial longitudinal temperature and salinity profiles were

taken from transect data during the period of interest.

Temperature and salinity profiles - hourly CTD data collected at stations 2, 8 and

12 were used for calibration.

Insolation - cloud cover data was taken from San Francisco airport and the hourly

insolation values were simulated.

Wind - no wind data was available during the period of interest so daily averages,

averaged over the study period were used. No hourly data was available.

River inflow - daily data were collected by Marin Municipal Water District.

Of the data used in the modelling, the bathymetry, temperature and salinity

profiles and transect data were considered reliable. The main problem in calibrating

and validating the model was the lack of water level data, both offshore and within the

estuary, required to correctly simulate estuarine hydrodynamics. Further calibration

and verification was difficult as the insolation and wind data were not from

measurements taken in the Tomales Bay region although the resultant match between

the modelled and observed temperature and salinity profiles was considered good

enough to make the sensitivity testing valuable. Obtaining two independent data sets

was not feasible within the time frame of the modelling, as the data sets collected

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within Tomales Bay were not concurrent and the data collected from other sources

was not readily available.

With the above-mentioned limitations, the objectives of the modelling were to

use the observational data to simulate the cold, upwelled water intrusions and density

current formation as accurately as possible and to test differing scenarios and their

effects on these intrusions. The value of this modelling is twofold: it lies in

determining the capability of the model to reproduce physical conditions within a

system which results in numerous predictive benefits, for example pollutant dispersal

within a system and secondly in determining the parameters important to Tomales

Bay during the summer long-residence season and how these parameters affect the

density current intrusions that are the sole source of ‘new’ water into the estuary

during this season. This analysis will then complete the second part of the research

questions posed in chapter 1 by describing how wind-driven coastal upwelling

influences the circulation and stratification within the estuary and providing

information of the sensitivity of this influence to differing physical conditions i.e.

tidal phase, insolation, wind, depth and ocean temperature. The following sections in

this chapter will describe the Delft3D model (section 7.1), describe the model

investigations, the model configuration and the optimisation of the model parameters

for the investigations (section 7.2) and then present the results (section 7.3),

discussion (7.4) and final conclusions of the modelling (7.5).

7.1 The Delft3D model

The Delft3D model developed by WL|Delft Hydraulics consists of different

sub-models or modules which simulate the time and space variations of six

phenomena, namely hydrodynamics (Delft3D-FLOW), wave refraction and shoaling

(Delft3D-WAVE), water quality (Delft3D-WAQ), morphology (Delft3D-MOR),

sediment transport (Delft3D-SED), and ecology (Delft3D-ECO) and their

interconnections. The model is suitable for a variety of conditions but is mostly used

for the modelling of coastal, river and estuarine systems. The Delft3D-FLOW

hydrodynamic model is a multi-dimensional (2D or 3D) hydrodynamic and transport

simulation program that calculates non-steady flow and transport phenomena

resulting from tidal and meteorological forcing (WL|Delft Hydraulics, 1999). This

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module of the Delft3D system was used to model the intrusion events at Tomales

Bay.

The Delft3D-FLOW model includes formulations and equations that take into account:

Tidal forcing; Wave-driven flows; Density gradients and forcing; Bed shear stress at the seabed (including wave effects); Drying and flooding on tidal flats; The effect of the earth’s rotation (Coriolis force); Free surface gradients (barotropic effects); Turbulence-induced mass and momentum fluxes.

The system of equations in Delft3D-FLOW comprise of the shallow water

equations derived from the 3D Navier-Stokes equations for an incompressible fluid

using the shallow water and Boussinesq assumptions as well as the continuity

equation. The equations and their numerical implementation are described in detail in

the Delft3D-FLOW user manual (WL|Delft Hydraulics, 1999), but simplified versions

of the equations used in the Delft3D-FLOW simulations are as follows:

Conservation of momentum in x-direction:

(7.1)

Conservation of momentum in y-direction:

(7.2)

Conservation of mass, also known as the continuity equation:

(7.3)

where η = water level elevation (m)d = still water depth (m)u,v = velocity in the x- and y-directions, respectively (m.s-1)U = magnitude of total depth-averaged current velocity (m.s-1)

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Fx,y = x- and y- components of external forces (Pa): surface and bottom stress

f = Coriolis parameter 2Ω sin θ, where Ω is the earth’s angular velocity

and θ is the geographic latitude (rad.s-1)

g = acceleration due to gravity (m.s-2)

ρ = water density (kg.m-3)

t = eddy viscosity (m2.s-1)

c = Chézy coefficient (m1/2.s-1)

The horizontal turbulent dispersive transport of momentum is computed using

a prescribed eddy viscosity coefficient. A quadratic friction law is assumed to give

the current shear stress (τ) at the seabed that is induced by turbulent flow:

(7.4)

where

|U| = the magnitude of the depth-average flow (m.s-1)

c = Chézy coefficient (m1/2.s-1)

In Delft3D-FLOW the Chézy coefficient may be determined according to

three different formulations, namely Manning’s formulation, the Chézy formulation

and White Colebrook’s formulation. For the Chézy formulation, the user specifies the

coefficient ‘c’.

In the horizontal direction an irregularly spaced, orthogonal, curvilinear grid

may be used. For 3D simulations the model uses the so-called sigma co-ordinate

approach in the vertical direction (WL|Delft Hydraulics, 1999). A sigma-coordinate

system scales the vertical coordinate relative to the local water column depth,

resulting in a constant number of layers over the entire model domain (Robson, 1999;

Van Ballegooyen and Taljaard, 2001). The relative layer thicknesses may also be

non-uniformly distributed to allow for increased vertical resolution in the region of

interest.

In highly stratified environments, methods to limit artificial mixing and

maintain sharp vertical gradients need to be optimised and are achieved in the

Delft3D-FLOW module through the use of the Alternating Direction Implicit time

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integration method, the cyclic or Van Leer-2 solution for the transport equation, a

sigma co-ordinate correction (that minimizes the artificial vertical diffusion and

artificial flow) and Forrester filters (Van Ballegooyen and Taljaard, 2001). The

accuracy of momentum propagation in the grid is related to the Courant number.

Van Ballegooyen and Taljaard (2001) successfully used the Delft3D-

FLOW model to simulate the hydrodynamics of the Kromme and Palmiet estuaries in

South Africa in order to determine the water quality of these stratified systems. In

the case of the Kromme estuary, the model was used to simulate the test release of

fresh-water from the Mpofu Dam into the system. In the Palmiet estuary, the model

was used to simulate the hydrodynamics under differing inflow conditions and mouth

states i.e. closed, semi-closed and open (Van Ballegooyen and Taljaard, 2001).

Nicholson et al. (1997) used the Delft3D-FLOW and -MOR to compare coastal

morphodynamic models showing that the model yielded a result that attained a steady

state of equilibrium, unlike models based only on the initial transport field.

7.2 Modelling of cold-water intrusion events

To help quantify the effect of coastal upwelling on the estuary, the Delft3D-

FLOW hydrodynamic model was used to simulate cold, ocean-water intrusion events

into Tomales Bay. This was motivated by the lack of observations of intrusion events

over a wide range of varying physical conditions. The model was used to simulate a

cold, ocean-water intrusion and to provide information on the strength of the intrusion

under varying scenarios. Dependence on a variety of parameters was explored: tidal

range, insolation, wind, fresh water inflow and bathymetry, as proposed in key

research questions 1.3.2 ii and iii. In the first instance the model was used to simulate

the intrusion that occurred from 16th – 18th June 1993. Observations were used to

calibrate and also verify the model for this event. This is referred to as the base case.

Further model runs were conducted to explore the sensitivity or dependence of these

intrusions on variations in the values of input parameters.

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7.2.1 Model investigations

The observed events are described in chapter 6.8. Although formation and

persistence is reasonably described by the data, the data is inadequate to resolve how

the strength and persistence of these events depend on tide, temperature differences,

wind, basin depth and other parameters. For this reason the Delft3D model was used

to address the following questions:

Tide: What effect does the tidal range have on the intrusion events? Is

increased mixing or increased intrusion associated with increased tidal

excursion?

Insolation: Will an increase in summer insolation aid vertical stratification and

thus enhance an intrusion by limiting vertical mixing?

Wind: In previous work, wind effect on the estuary has been ignored because

Tomales Bay is considered a comparatively sheltered environment (Largier et

al., 1977; Robson, 1999). Is this valid? Winds can set up pressure gradients

due to the tilt of both the surface water levels and isopycnals and can bring

about vertical mixing.

River inflow: Does fresh-water inflow have an effect on the summer

intrusions by: increasing stratification or increasing vertical mixing or by

causing a seaward tilt to the surface?

Depth: Will a change in the estuary depth have an effect on the intrusions?

Deeper depths should allow easier intrusion of cold water.

Ocean temperature: Do colder waters lead to stronger cold-water intrusion

events? Colder, denser water should lead to greater stratification and larger,

more stable intrusions.

A total of 15 runs were conducted and the simulations are listed in table

7.2.1.1. The ‘base case’ is the run that simulates the cold, ocean-water intrusion event

observed from 16 – 18 June 1993 (run 1). The other simulations involve an increase

or decrease in one of the 6 parameters listed above, while others remain at base

values. Parameters are adjusted to levels 25 % higher or lower than base values

unless otherwise stated (indicated in brackets). Only one parameter is adjusted at a

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time and there is no exploration of the effects on interaction between parameter

influences.

7.2.2 Model configuration

Bathymetry

Digital Tomales Bay bathymetry (relative to MLW) was retrieved from the

National Ocean Service, N.O.A.A., U.S.A. Bodega Bay bathymetry was digitised

from the N.O.A.A. nautical chart number 18643, relative to MLLW. Both sets of

bathymetry data were converted to a flat-space projection using LO co-ordinates and

corrected to MSL using a Java Vdatum program provided by Dr. D. Milbert from

N.O.A.A. The model requires positive LO co-ordinates and so the LO co-ordinate

reference frame was converted to a local co-ordinate reference frame by adding the

following arbitrary values to the co-ordinates:

x + 10 000 and y – 4 200 000.

The bathymetry used in the model is shown in figure 7.2.2.1.

Grid

A rectilinear grid with 10 layers in the vertical direction was set up over the

estuary (figure 7.2.2.2). The model with a rectilinear grid reasonably represents the

observed patterns and it was decided little would be gained by using a curvilinear grid

for this application. The grid was set up as follows:

i) The grid was refined in the “outer” region (0 – 6 km) with cells: 80 x 100 m.

ii) The grid in the “middle” region (6 – 12.5 km) had cells: 80 x 200 m.

iii) The grid was coarsest near the “head” (> 12.5 km), away from the region in which

the cold-water intrusions occur, with cells: 80 x 300 m.

Dry cells were inserted where the bathymetry values were above zero. The

observation cells, representing the data collection stations, used to verify the model

are indicated in red on figure grid. Starting at the mouth, the red nodes indicate the

mouth, station 2, station 8 and station 12.

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Ocean-estuary open boundary

The offshore boundary (2 780 m offshore from the mouth) was simulated as

an open water level boundary. Observed water levels from Horseshoe Cove (northern

end of Bodega Bay) were referenced to MSL and used as the boundary conditions for

Bodega Bay water levels. Observed surface temperature and salinity time series

values for Bodega Bay were input as a uniform profile at the ocean-estuary boundary

(figure 7.2.2.3).

Meteorology

The atmospheric data used for the model was net incoming solar radiation.

Clear sky solar radiation was determined as: no sky solar radiation values that were

reduced by a factor of 0.7145 (which is the calculated transmissivity of the

atmosphere based on the consistency Seckel and Beaudry (1973) daily clear sky short

wave radiation values (Reed, 1977)). Simulated solar radiation for cloudy skies was

determined using the observed cloudiness at San Francisco National Airport:

, (7.5)

where the first term = albedo and the second term = cloud factor.

Qsn gives the actual solar radiation entering the surface waters.

Qan = (1 - 0.03) x (1 + 0.17 x cld) x (218 + 6.3 x Tair) (7.6)

where Tair = air temperature and Qan is an indication of the atmospheric back radiation

based on measured air temperatures (Wm-2).

The total radiation in (Wm-2) is Qsn + Qan and is what was used in the model (figure

7.2.2.4).

Wind

No wind data for Tomasini Point was available over the 16 – 18 June 1993 so

the daily wind speeds and directions averaged over the study period at Tomasini Point

were used in the model. To simulate observed conditions, the wind was switched on

until 17th and then switched off (figure 7.2.2.5).

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Model calibration and verification

Calibration and verification (comparison of the modelled and observed water

levels and temperatures at stations along the estuary) of a model requires two

independent data sets, one of which is used to calibrate the model and the other to

verify the results (Van Ballegooyen and Taljaard, 2001). Typically the calibration is

performed using water level and current velocity data taken from a number of sites

along the estuary. Pressure sensor data at station 12 was used as a direct measure of

water level in that region, although no correction for atmospheric pressure was

possible. The model was calibrated by visually comparing modelled and water levels

on the simulated days (figure 7.2.2.6).

Figure 7.2.2.6 Calibration of the modelled hydrodynamics using recorded pressure

data for water levels at station 12. Observed water levels, modelled

water levels.

Temperature data at stations 2, 8 and 12 were then used as further calibration data for

the model output (figure 7.2.2.7). No verification was possible as there was no

complete second available data set at the time of this project. Although the

hydrodynamics were not completely resolved, the calibration of the model data

showed an acceptable level of agreement

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that the simulation of the cold ocean water intrusion and the parameter dependence

study was not compromised.

7.2.3 Optimisation of model parameters for Tomales Bay

Advection scheme

In order to conserve the steep vertical gradients without the generation of

spurious oscillations, the solution method used for the transport equation was the

cyclic method. Forester filters were also used as a method to remove non-physical

oscillations in regions of steep gradients (Van Ballegooyen and Taljaard, 2001). The

vertical Forester filter was used to inhibit artificial vertical mixing and remove

oscillations of temperature, salinity and other constituents in the vertical.

Time step

The 3D shallow water flow equations are solved using the alternating direction

implicit time integration method. This method is unconditionally stable. However, to

ensure accurate wave propagation in the grid and an accurate solution, the Courant

number should not typically exceed 10 - 30 (Van Ballegooyen and Taljaard, 2001).

The time step was chosen to meet this criterion and was set at 0.5 minutes.

Wetting and drying algorithm

The FLOW package includes a wetting and drying algorithm and a value of

0.1 m was specified to ensure that the grid cell was ‘wet’ only after the water had

risen to that level. This is to avoid repeated wetting and drying of cells with each

successive time step and thus avoids spurious oscillations in the numerical results

(Van Ballegooyen and Taljaard, 2001).

Number of vertical layers

The number of vertical layers is important for the resolution of the maximum

vertical gradient (temperature, salinity and density) of the water column during

stratified conditions. Inadequate resolution results in artificial mixing and the

breakdown of the thermocline (Van Ballegooyen and Taljaard, 2001). Van

Ballegooyen and Taljaard (2001) suggest that the minimum number of layer should

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exceed 3 times the maximum vertical temperature gradient i.e. . A vertical

resolution of 10 layers was used in the simulations.

Vertical viscosity

The magnitude of the vertical viscosity determines the amount of vertical

mixing across the pycnocline. Low values ( 10-6 m2s-1) are indicative of decoupled

flows. Values of 10-4 m2s-1 are an indication of flows that are more strongly

coupled, resulting in a decrease in the velocity shear at the pycnocline (Van

Ballegooyen and Taljaard, 2001). Vertical viscosity values of 10-6 m2s-1 were used

during the simulations. Although values can be stipulated at the start of the

modelling, values cannot be altered during the modelling using Delft3D, for example,

reduced mixing during stratification.

Turbulence closure scheme

Pycnocline dynamics have been observed to be best modelled using the k-ε

turbulence closure scheme as it shows improved mixing characteristics over other

schemes e.g. algebraic (k-L) turbulence scheme (WL|Delft Hydraulics, 1999).

Thatcher-Harleman condition

The FLOW package allows for the possibility that some of the water that

leaves the estuary on the ebb tide may re-enter the estuary with the following flood

tide by using the Thatcher-Harleman condition that specifies an appropriate time scale

to characterise this effect (Van Ballegooyen and Taljaard, 2001). A Thatcher-

Harleman condition of 60 minutes was used during the modelling.

The optimal parameters used for the simulation of Tomales Bay

hydrodynamics are summarised in table 7.2.3.1.

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Parameter Value

Time step 30 seconds

Wetting and drying threshold 0.1 m

Number of vertical layers 10

Horizontal viscosity 1.0 m2s-1

Vertical viscosity 1.0 x10-6 m2s-1

Horizontal diffusivity 1.0 m2s-1

Vertical diffusivity 1.0 x10-6 m2s-1

Chézy coefficient 55 m1/2 s-1

Turbulence closure model k-ε turbulence closure

Advection scheme Cyclic method

Sigma-coordinate correction On

Forrester filer vertical On

Forrester filter horizontal Off

Atmospheric heat flux model Net incoming solar radiation

Table 7.2.3.1: Optimal parameters used for the simulation of Tomales Bay

hydrodynamics.

7.3 Results

The model simulation of the cold water intrusion event over 16 – 18 June 1993

is shown in figure 7.2.2.7, where the event can be seen occurring at the bottom of

station 8 on the 16th June and is observed at the bottom of 12 on the 17th June 1993.

The event was not fully reproduced at the bottom of station 8 (although the intrusion

is still observed) but is well represented at the bottom of station 12. The lack of data

for calibration of the model prevented any further improvement of the hydrodynamics

and the best fit to the data the region of station 8 was plotted. However, this was not

considered limiting as the value of the modelling scenarios lies in their contribution to

the understanding of the summer dynamics / circulation of Tomales Bay under

differing conditions. Their value is highlighted by determining the extent of the input

parameter influence on the estuary, especially in examining processes previously

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thought to have no impact on the summer circulation e.g. wind and fresh-water

inflow.

Figure 7.3.1 shows ‘snapshot’ transects of the formation of the density current

intrusion for the base case (run 1). The avi transect of the temperature and density for

the ‘base case’ indicates the modelled density current intrusion along the estuary

(figure 7.3.2, on the cd). The transect station positions are indicated below:

Offshore boundary = 0 m

Station 0 (entrance) = 2 780 m

Station 2 = 4 780 m

Station 6 = 8 780 m

Station 8 = 10 780 m

Station 10 = 12 780 m

Station 12 = 14 780 m

Station 16 = 18 780 m

Station 18 = 20 780 m

The inflow of cold, upwelled water moves into the estuary with the flood tide.

Although the cold water is pushed seaward with the ebb tide, the denser water plunges

beneath the less dense estuarine water and a density current propagating landward is

observed (figure 7.3.2).

Surface velocity plots (figure 7.3.3) are indicated to further verify the model

results. The avi of the tidal velocities is shown in figure 7.3.4 on the cd. The velocity

section yields results as expected where the tidal velocities are at a maximum near the

mouth region of the estuary (especially along the channel) and rapidly decrease in

magnitude landward of station 6. The flow is primarily concentrated along the

western side of the estuary, although some flow in a deeper ‘channel’ around the

shallow areas in the outer region is observed for both the flood and ebb tides.

The parameter sensitivity model results and comparisons with the base case

are shown in figures 7.3.5 – 7.3.10.

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Tidal effect

An increase in the tidal range of 25 % (run 2, maximum tidal range 2.9 m)

caused a small decrease ( 0.1 C) in water temperature at station 2 (figure 7.3.5).

The maximum tidal range of the base case was 2.3 m. The water temperature at the

surface of stations 8 and 12 was continuously cooler than the case case from 17 th at

22h00 onwards. The bottom of station 8 was cooler at all times except peak ebb and

the bottom of station 12 was continuously cooler from the 17th at 12h00 onwards. The

reverse pattern was observed for an average tidal range (run 3, maximum tidal range

1.7 m), where the water was typically warmer than the base case (figure 7.3.5). A

density current is observed during both runs 2 and 3 at stations 8 (starting on the 16 th)

and 12 (starting on the 17th), where the vertical stratification is initially increased

(decreased), at the start of the events, with an increase (decrease) in tidal range. No

density current was observed over neap conditions (run 4, maximum tidal range =

0.92 m).

Effect of insolation

Both an increase in insolation (run 5) and an absence of any insolation (run 6)

had a dramatic effect on the water column temperature (figure 7.3.6). A 25 %

increase in insolation resulted in an increase of water temperature at station 2 and the

surface and bottom of stations 8 and 12. The opposite was true for the decrease in

insolation. An increase in insolation had an impact at all stations throughout the

modelled period (15 – 22 June 1993), but a decrease in insolation was observed to

have a greater impact at the surface and bottom of stations 8 and 12 once the event

occurred. An event was observed for both runs at the bottom of stations 8 and 12.

Water column stratification (taken on the 17th at 22h00) increased with an increase

in insolation and decreased with a decrease in insolation (table 7.3.1).

Stratification Run

Station Base case Run 5 Run 6

Station 8 3.2 C 5.5 C 3 C

Station 12 2.8 C 3.2 C 2.7 C

Table 7.3.1: Vertical stratification on 17th June 1993 at 22h00 for stations 8 and 12

for the simulated increase in warming (run 5) and no solar heating (run 6).

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Wind effect

A continuous wind caused a decrease of the water temperature at station 2 and

at the surface of stations 8 and 12 (run 7, figure 7.3.7). On average, an increase in

water temperature occurred at the bottom of stations 8 and 12 with an increase in

wind speed. No density current event was observed for run 7. Strong winds (> 15

ms-1; run 9) resulted in a decrease in water temperature throughout the water column,

throughout the estuary. No density current was observed during strong wind

conditions. No wind (run 8, figure 7.3.7) resulted in warmer water at station 2 and the

surface of stations 8 and 12 and colder water at the bottom of stations 8 and 12 until

the expected start of the intrusion event where the water was warmer than the base

case. The event occurred as soon as cold water was present at the mouth during run 8.

Wind directions are shown in table 7.3.2.

Date 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Wind direction 312 301 313 313 300 314 309 311 310 312 309 311 302 152

Table 7.3.2: Wind directions for over 8th – 21st June 1993 for runs 7 and 9.

Effect of fresh water inflow

Constant low (< 1m3s-1, run 10) and pulsed (>20 m3s-1 on 17th and 18th June

1993, run 11) fresh water inflow had no significant effect on the formation of the

density current (figure 7.3.8) i.e. did not increase the vertical stratification.

Depth effect

The water temperature at station 2 remained the same over flood tide but the

was warmer over the HLW ebb tide with an increase in depth (run 12, figure 7.3.9).

The water temperature was colder at both the surface and bottom of stations 8 and 12

during the density current intrusion event. A decrease in depth (shallower estuary)

resulted in warmer water temperatures and a phase shift at station 2 (run 13, figure

7.3.9). In general, warmer water temperatures were observed at the surface and

bottom of stations 8 and 12. Density currents were observed for both runs 12 and 13.

Ocean temperature effect

An increase in the temperature of the ocean water caused an increase in the

temperature observed at all stations (runs 14 and 15). The effect is observed more

strongly at the bottom stations where the density current intrusion event no longer

occurs (figure 7.3.10).

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7.4 Discussion

Cold, ocean water intrusions appear to be a dominant small-scale feature

within Tomales Bay if the initial conditions for their formation are met. With cold

water at the mouth of Tomales Bay and a large enough tidal range, a density current

forms and intrudes landwards, persisting while there is a supply of cold water to the

plunging area (figures 7.3.1 and 7.3.2). Figure 7.3.2 indicates the landward

progression of the density current through the tidal cycle over 15 – 22 June 1993,

while the velocity section shows the tidal velocities that result in the observed

conditions (figures 7.3.3 and 7.3.4).

All of the tested input parameters had an effect on the intrusions, either

decreasing or increasing the strength of the vertical stratification but only neap tidal

conditions, an increase the wind speed and the lack of cold water in the plunging area

resulted in the break down of the modelled density current intrusion.

An increase in tidal range results in an increased tidal excursion and the cold

water is moved further into the estuary on the flood tide, resulting in cold water

entering further into the estuary and a slightly stronger density current (figure 7.3.5).

This effect is evident at station 8. The warmer bottom water at station 12 (than station

8) indicates that mixing with the estuarine water is occurring with the landward

propagation of the density current, as the difference in temperature at station 12 from

the base case is less than the difference between that at station 8. Such an extreme

tidal range ( 2.9 m) may have inhibited the formation of a density current through

tidally induced vertical mixing of the water column. This does not occur, indicating

that the tidal velocities are not able to vertically mix the water column landward of

station 8, despite the significant increase in tidal excursion. The opposite occurs with

a decrease in tidal range. Cold water does not enter as far into the estuary and the

volume of cold water supplied to the plunging area is less and thus the strength of the

density current is reduced. No density current intrusion developed, under neap tidal

conditions, as the cold water did not reach the plunging area 6 km into the estuary.

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A change in the insolation had the greatest impact on the water column (figure

7.3.6). Increased insolation dramatically increased the vertical temperature

stratification of the water column (by 2.3 C at station 8 and 0.4 C at station 12, from

the original). As the density current forms, the water column stratifies. An increase

in insolation on a stratified water column primarily affects the surface layers of the

water column and the vertical temperature stratification is increased. This strengthens

the density current by inhibiting the vertical mixing within the water column,

however, some diffusion of heat or vertical mixing does occur as the bottom water

was observed to be warmer than for the base case. Summer intrusion events are thus

expected to be stronger than those occurring during spring due to the summer increase

in insolation. Although not entirely realistic, the simulation of no insolation had a

large impact on the water temperature of the entire estuary. Water temperatures were

colder throughout the estuary, decreasing both the vertical temperature stratification

(by 0.2 C at station 8 and 0.1 C at station 12, from the original) and the longitudinal

density gradient required to drive the density current. Consequently, the density

current was weakened.

The wind was observed to have a significant effect on the estuary and on the

density current formation. The presence of a continuous wind prevented a density

current from forming by vertically mixing the water column at both stations 8 (depth

5.4 m) and 12 (depth 7.6 m, figure 7.3.7). Although the wind mixing prevented the

development of a density current, the water column was not completely mixed. Only

under stronger wind (> 15 ms-1) conditions did the water column completely vertically

mix. Conditions of no wind resulted in warmer surface water due to the lack of

mixing with cooler underlying water. Cold water intruded into the estuary but the

density current formed as soon as cold water was present in the plunging area. The

density current occurred 2 days earlier for run 8 than the base case as cold water was

present in the estuary and there was no wind to initially mix the water column and

delay the start of the intrusion (the intrusion is not evident at the bottom of station 8 as

it would have occurred on 14th June 1993). This implies that along with insolation,

the wind plays an important role in the timing of the development of density currents

within the estuary. Where the insolation strengthens the intrusion by increasing the

vertical stratification, the wind controls both the timing of the event and where winds

increase, the break down of the events through wind mixing of the water column.

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Regardless of fresh water inflow into the estuary, density currents form. Both

constant low inflow (typical summer conditions) and pulsed inflow (e.g. summer dam

release) resulted in little to no change in the landward propagation of the density

current (figure 7.3.8) and the expected increase in stratification did not occur. Winter

fresh-water inflow typically moves through the estuary as a surface outflow, vertically

stratifying the water column. The lack of result of runs 10 and 11 may be due to the

model distributing the fresh water inflow throughout depth into the estuary – although

a surface discharge was specified. The pulsed fresh-water inflow was expected to

increase the vertical stratification of the water column and thus increase the strength

of the density current. Since the head of the estuary (fresh-water input region) is

extremely shallow (< 2 m), the water column is mixed as inflow occurs and this water

moves seawards, as a mixed water column, mixing with the ambient estuarine water.

The inflow did not flow over the surface of the estuarine water – as expected. Fresh-

water inflow primarily affects the salinity of the water column. Since the density

current intrusions are temperature driven, the effect of the fresh-water inflow was not

observed.

An increase in depth made no obvious difference to the ease with which the

water enters the estuary on the flood tide but did help the tide to ebb i.e. the water was

not trapped within the estuary (figure 7.3.9). The colder water observed at stations 8

and 12 indicates that the cold water was entering the estuary with less frictional

retardation with the increased depth and the vertical temperature stratification

increased, increasing the strength of the density current. A decrease in depth i.e. a

shallower estuary resulted in an increase in the exposed (dry) regions of the estuary.

The total volume of water entering and leaving the estuary with the tide remains the

same but the cross-section through which the water flows has decreased and thus the

tidal velocities increase to compensate. This resulted in increased vertical mixing

over both the flood and ebb tides. For a density current to move landward, the

baroclinic propagation speed must be comparable to, if not greater than, tidal

velocities. The lack of development of a density current in the shallower estuary

implies that the propagation speed of the density current is no longer comparable to

the tidal velocities and even though cold water is present at the plunging region and

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enters the middle region with the flood tide, the ebb tide velocities either vertically

mix the water column or flush the cold water seawards.

As expected, the ocean water temperature plays a vital role in the formation of

density currents in the estuary (figure 7.3.10). No density current intrusion will form

if there is not a strong enough density gradient to drive the intrusions. That is why

one of the pre-requisites to a density current intrusion is the presence of cold,

upwelled water at the plunging area. Although the cold water is typically present at

the mouth of the estuary throughout March – November, the strongest temperature

gradients are established through insolation. This potentially limits these intrusions to

the spring summer upwelling period along this region of the California coastline.

7.5 Conclusion

The Delft3D-FLOW model resolved the dynamics of cold, ocean water

intrusions into Tomales Bay in detail. The formation of these intrusion events relies

on the presence of cold, upwelled water at the plunging area and are thus restricted to

periods of coastal upwelling i.e. spring and summer along this region of the California

coastline, and a tidal range capable of moving 6 km into the estuary on the flood

tide. The modelling has shown that the persistence and removal of the density current

is affected by other parameters, to varying degrees. Even an extreme tidal range for

this region (tidal range = 2.9 m) resulted in a density current intrusion and in fact,

strengthened the intrusion, with the reverse being true for a decrease in tidal range

where no intrusion occurred under neap conditions where the cold, upwelled water

did not reach the plunging area. Summer insolation was observed to strengthen the

vertical stratification and although insolation does not result in the formation or break

down of density currents, intrusion events are likely to be stronger during summer,

when the seasonal insolation (and thus vertical stratification) is at its peak. A

decrease in solar heating decreases both the vertical and horizontal density gradients,

decreasing the strength of the density current, indicating that intrusion events are

likely to be weaker in spring. After the tide, the wind appears to have the greatest

impact on density current intrusions. Wind of sufficient speed vertically mixes the

water column in the middle and inner regions of the estuary and thus inhibits the

development of or breaks down an existing density current. Since the middle and

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inner regions of Tomales Bay are shallow, ‘weak’ wind speeds (15 ms-1) were able to

vertically mix the water column, especially since the estuary is typically vertically

mixed throughout summer and only stratifies during intrusion events. Low inflow

and pulsed fresh water inflow had no impact on density current intrusions, implying

that any controlled summer dam release of fresh-water into the estuary would not

impact the intrusion of nutrient rich water into the estuary as a density current. Any

impact, on density current intrusions, due to fresh-water inflow may be expected for

high inflow volumes (e.g. flood conditions), especially during periods of high

insolation, where the fresh water would flow seawards as a surface layer, enhancing

vertical stratification, thus potentially strengthening the intrusion of density currents.

The depth of the estuary is another important factor where a decrease in the depth

may inhibit the formation of density currents through flushing of the cold water out of

the estuary with the ebb tide or mixing of the water column due to increased tidal

velocities. Tomales Bay is thought to have reached a present day stable state with

regard to depth (Smith S.V. et. al., 1996) although infilling does still occur but at a

much reduced rate (Rooney and Smith, 1999). Substantial infilling has previously

occurred as discussed by Hearn and Largier (1997) and Rooney and Smith (1999) and

should this re-occur the circulation within the estuary would be altered and this is

likely to be detrimental to the currently “pristine” status of the system as these

summer intrusions are the sole source of “new” water and nutrients into the estuary

during the 3 month summer residence period.

The second part of the research questions have thus been answered through the

use of the Delft3D model in simulating the effect of wind driven coastal upwelling on

the estuary and the resulting estuarine stratification and circulation. Where the

observational data indicated the occurrence of density currents within the estuary

during spring and summer, the modelling was able to provide information on the

sensitivity on the formation and persistence of a density current, under varying

physical parameters. The modelling has thus completed the analysis of the effect of

the intrusion of cold, upwelled water into Tomales Bay and has enabled the research

objective to be achieved. The model adds additional value to the thesis in its

capability to successfully reproduce physical conditions within this type of system i.e.

a system where sharp vertical and horizontal gradients are important to the processes

occurring within the system. This has numerous predictive benefits, essential for the

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management of these systems, as the modelling enables limited (but still specific) data

collection to be sufficient in understanding estuarine circulation rather than relying

solely on previous methods of extensive data collection and observations. The

modelling is thus a valuable tool that compliments observational methods in the

understanding, and consequent management, of estuarine systems.

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8lmer.marsci.uga.edu/tomales_data/Thesis/chapter7.doc · Web viewIn order to conserve the steep vertical gradients without the generation of spurious oscillations, the solution method