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 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 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 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 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)

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)

nt = 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 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.

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.