MODELLING FLOW AND WATER QUALITY IN ESTUARINE AND RIVERINE WATERS: A DYNAMICALLY LINKED 1-D AND 2-D MODELS APPROACH

B. Lin, S. M. Kashefipour, E. Harris and R. A. Falconer

School of Engineering, Cardiff University, Cardiff, UK

Tel: +44 29 2087 4696, Fax: +44 29 2087 4597, E-mail: Linbl@cardiff.ac.uk

Abstract: Details are given herein of a numerical model study aimed at quantifying the impact of various bacterial inputs into estuarine and riverine waters on the bathing water quality. In this study faecal coliform has been used as the water quality indicator organism. The numerical model developed for this study combines a depth integrated two-dimensional coastal model and a cross-sectionally integrated one-dimensional river model, capable of predicting the water surface elevation, velocity and faecal coliform distributions simultaneously across the entire model domain. The model was then applied to a large estuary, namely the Ribble Estuary, UK, and calibrated using water level, velocity and faecal coliform concentration measurements from six surveys. In order to predict the faecal coliform concentration distribution, variable decay rates were used, i.e. different values for the decay rates were applied to sea and riverine waters, during day and night time hours and wet and dry weather conditions.

Keywords: water quality, faecal coliform, decay rate, numerical modelling, estuaries, rivers

1    INTRODUCTION

Since the prevailing velocity structure in river flows is generally one-dimensional (1-D) the governing hydrodynamic and solute transport equations written in 1-D form are usually used for modelling flow and water quality indicators in riverine systems. In estuarine and coastal waters, where a dominant flow direction does not exist, then depth averaged two-dimensional (2-D) models are generally applied for flow and water quality modelling. For many engineering projects both riverine and estuarine waters are involved and the main interest is to determine the impact of the various inputs discharging into the rivers on the estuarine and coastal water quality. Hence it is necessary that water elevations, velocities and water quality concentrations are calculated simultaneously in riverine and estuarine waters.

The paper describes the development of a linked numerical model for predicting the tidal currents and faecal coliform distributions in an estuarine and riverine system. The model has been used for the Fylde Coast and Ribble Estuary study (see Figure 1) to assess the impact of various bacterial sources on the receiving coastal waters. The model domain comprises a range of topographic and bathymetric features, varying from wide-open sea to narrow river channels. The linked model is capable of predicting the water surface elevation, velocity and water quality indicators across the entire modelling domain simultaneously.

Faecal coliform has been used as the governing water quality indicator in this study. The decay rate of faecal coliform controls the fate of this micro-organism, thus it is one of the key factors affecting the accuracy of the model prediction. To achieve a more accurate prediction of the faecal coliform concentration different faecal coliform decay rates were applied for sea and riverine waters, day and night times and wet and dry weather conditions. Details are given of the model calibration against field measurements from six surveys. The model was then applied to predict the impact of various capital investment plans on the bathing water quality.

Fig. 1  Fylde Coast, Ribble Estuary and its tributaries

2    NUMERICAL MODEL DETAILS

The mathematical models used in this project include a 1-D model, FASTER (Flow And Solute Transport in Estuaries and Rivers), and a 2-D model, DIVAST (Depth Integrated Velocity And Solute Transport).

The FASTER model, which can be used to simulate hydrodynamic, solute and sediment transport processes in well-mixed rivers and narrow estuaries, has been developed based on the solution of the St Venant equations through an implicit finite difference scheme, with a varying grid size over a space-staggered grid. The water quality module of this model was developed based on a finite volume solution of the advective diffusion equation proposed by Kashefipour and Falconer (1999).

DIVAST was developed for simulating hydrodynamic, solute and sediment transport processes in estuarine and coastal waters. The hydrodynamic module was developed based on the solution of the depth integrated Navier-Stokes equations. For the water quality and sediment transport module, the two-dimensional advective-diffusion equation was solved for a range of water quality indicators using the highly accurate ULTIMATE QUICKEST scheme (Lin and Falconer, 1997).

The faecal coliform (FC) bacteria group is indicative of organisms from the intestinal tract of humans and other animals. In recent years several investigators have used faecal coliform discharging through outfall and/or non-outfall sources to quantify the quality of bathing water and urban river waters (Wyer et al, 1997, and Thackston and Murr, 1999). In modelling faecal coliform the decay term is generally expressed as a first order decay function. Several factors such as sunlight, temperature and salinity level may influence the population of the organisms in a water body and thus in reporting the decay rate sampling conditions are usually specified. In the literature there is a large variation in the range of decay rate values for faecal coliform. Anderson et al have reported the decay rate to be in a range of 0.08 to 2.0 day^-1 for E.coli in seawater conditions, whereas Fujioka et al have reported that for faecal coliform the decay rate was in a range of 37-110 day^-1 in seawater and for sun-light conditions. The faecal coliform decay rate was also reported in the range of 0.0 to 6.1 day^-1 for different conditions of salinity and sunlight (see Thomann and Mueller, 1987).

3    A DYNAMICALLY LINKED 1-D AND 2-D MODEL APPROACH

The main interest of this study was the water quality of the EC designated bathing waters located at the mouth of the Ribble Estuary. In order to reduce the possible inaccuracies caused by setting up the boundary conditions required by the numerical models, the upstream boundaries were extended to the tidal limits of the rivers Ribble, Darwen and Douglas (Figure 1) and the downstream boundary was located around the 25 m depth contour in the Irish Sea. The length of the seaward boundary was 41.2 km, but the width of the river boundaries were generally less than 10 m. Such a large variation in the modelling scale makes it impractical for either a 1-D or 2-D model to be used alone. Applying each of these two models individually or linking the models statically could introduce inaccuracies in the model prediction results and lead to a considerable amount of extra effort to exchange the data. Thus, in this study the 1-D FASTER and 2-D DIVAST models were linked dynamically to form a single model, in which the hydrodynamic parameters and water quality indicators were computed simultaneously for the entire modelling region.
In this combined model the two sub-models were run individually at each time step and the required boundary values were exchanged between the 1-D and 2-D models in the common area (see Figure 2). For the hydrodynamic modelling the water surface elevations predicted from the 2-D model were provided as the downstream boundary conditions in the 1-D model and the velocity predicted by the 1-D model was used as the upstream boundary condition of the 2-D model. In water quality modelling the predicted faecal coliform concentration from the 2-D model was used in the 1-D model when the flow at the 1-D model boundary was directed landwards, whereas the predicted faecal coliform concentration from the 1-D model was passed to the 2-D model when the flow at the 2-D boundary was directed seawards. Therefore, for the hydrodynamic modelling the external boundary conditions required were water elevations at the seaward boundary and discharges at the landward boundaries (i.e. the tidal limits); whereas for water quality modelling measured faecal coliform concentrations were given at the landward boundaries.

Fig. 2    2-D Boundaries and overlap region between 2-D and 1-D models

4     MODEL APPLICATION AND FIELD DATA

The linked model was then applied to assess the bathing water quality in the Ribble estuary and Fylde Coast. This estuary is situated along the north-west coast of England, in the county of Lancashire. At the mouth of the estuary there are two well renowned seaside resorts, namely Lytham St Annes and Southport, with both being designated EC bathing waters. The Fylde Coast, which is limited in the north by Fleetwood and in the south by the Ribble Estuary, is one of the most famous seaside resorts in England for family holidays, particularly the City of Blackpool, hosting on average more than 17 million visitors a year.

The model domain consists of 850 km² of estuarine and coastal area (2-D model) and about 41 km of river channels (1-D model). The 1-D model contains 1075 cross-sections distributed on 5 riverine reaches, with the distance between two consecutive cross-sections being generally less than 50 m. To ensure a reasonable resolution at the upstream boundary of the 2-D model, the grid size was chosen to be 66.7m ´ 66.7m.

An extensive programme of field data collection was also undertaken by the UK Environment Agency to provide data for calibration and verification of the model. The bathymetric data used in this study was primarily obtained using three methods: (i) conventional surveying techniques; (ii) LIDAR (Light Induced Direction And Range); and (iii) side-scan sonar. In the deep waters just beyond the Ribble mouth, bathymetric data were digitised from the Admiralty Chart.  These data were combined using linear interpolation to form the bathymetric data for the whole Ribble model.

                            Table 1     General information of surveys

Six comprehensive sets of hydrodynamic and water quality data were collected during the winter period of 1998 and the summer period of 1999 to include a combination of weather and tide conditions. The general conditions for the surveys are summarised in Table 1. During each survey, measurements were taken at all discharging locations and river upstream boundaries (tidal limits) for two consecutive days. In total 34 input sources were identified that contributed to the pollution issues of this estuary. These included: direct discharges of treated wastewater from treatment plants and inputs from the upstream boundary of 3 major rivers, several small rivers and combined sewer overflows. Details of the measurements undertaken at these sources can be found in Kashefipour et al (2000). Four calibration points were chosen along the main channel of the Ribble including: 11milepost, 7milepost, 3milepost and Bullnose (see Figure 1). Measurements at these locations were taken only for the second day of a survey.

Measured discharges at the upstream tidal limits of the rivers Ribble, Darwen and Douglas were used as the upstream open boundary conditions and the predicted water levels from the Irish Sea model purchased from the Proudman Oceanographic Laboratory (POL) were used as the seaward boundary conditions.

5    RESULTS AND DISCUSSIONS

The main parameter used for hydrodynamic model calibration was the bed roughness. The model was calibrated by choosing the best fit between the model predicted results and the measured data for different bed roughness values. In the Ribble model different roughness values were used along different reaches of the model domain to reflect the local conditions. For the open sea waters it was found that the best roughness value , or the Nikuradse equivalent sand grain roughness, was 20 mm. For the 1-D zone the Manning roughness coefficient was used and values ranged from 0.021 for the lower part of the river to 0.028 for the upper part of the river.

Fig. 3    Comparison of predicted water elevations and currents with measured data at: (a) 7milepost, and (b) 3milepost for an event on 19 May 1999

Since the fate of faecal coliform is influenced by many factors, calibration of the water quality model is generally more difficult than that of the hydrodynamic model. The accuracy of the model prediction depends not only on the accurate representation of the advection and dispersion processes, but also on the decay rate used. The selection of the decay rate is controlled by many external conditions such as light intensity, water temperature, salinity level and etc. The average decay rates (at 20^°C) used were found to range from a minimum value of 0.71  ( =77.8hr) for wet weather events to a maximum value of 2.32 ( = 23.8hr) for dry weather events. This range in the decay rate is comparable to typical values reported in the literature (Thomann and Mueller, 1987).

In general, good agreement was obtained between the model predictions and the measured data for both the hydrodynamic and water quality calibrations. Figure 3a illustrates a comparison of the predicted and measured water elevations and current speeds and directions at 7milepost (2-D region) for an event on 19^th May 1999. Figure 3b shows a similar comparison for 3milepost (1-D region). Figures 4a and 4b show comparisons of the predicted and measured faecal coliform concentrations at 7milepost and 3milepost respectively for an event on 19^th May 1999. The average errors in the water elevation and velocity field predictions for all of the events considered (see Table 1) and all four calibrating sites including: 11milepost, 7milepost, 3milepost and Bullnose were 0.18m and 0.14m/s, respectively.

Fig. 4    Comparison of predicted and measured faecal coliform concentrations for survey on 19^th May 1999 at: (a) 7milepost, and (b) 3milepost

6    CONCLUSIONS

Details are given of development of a numerical model, which links a one-dimensional river model with a two-dimensional coastal model for modelling the flow and water quality in riverine and coastal waters simultaneously. This linked model was then applied to the Ribble Estuary and Fylde Coast, UK, to simulate the impact of faecal coliform inputs discharging into the rivers, upstream of the estuary and coastal area. Comparisons between the predicted results and measured data were encouraging. The main conclusions drawn from this study can be summarised as follows:

l       The dynamically linked model approach is useful in modelling complex riverine, estuarine and coastal systems. This approach increases both the accuracy of the model prediction and the efficiency of setting-up and running the numerical model.

l       Comparisons of the model predictions against measured data showed that the model was able to predict accurately the water elevation, velocity and water quality indicator distributions.

l       The value of the decay rate for faecal coliform was influenced by many factors and the use a varying decay rate is important for prediction of faecal coliform concentrations. It was found that the die-off is faster in day time than at night and in dry rather than wet weather conditions. The maximum and minimum faecal coliform decay rates used were 2.32 and 0.71 day^-1 at 20°C for dry and wet weather conditions respectively.

Acknowledgements

This research study was funded by the North West Water Ltd (NWW) with the assistance of the Environmental Agency, North West Region. The authors would like to express their thanks to Julie Wakeham of North West Water Ltd and Andrew Wither, Michael Westen, Andrew Hartland and Hanner Green of the Environment Agency.

References

[1]  Lin, B., and R.A. Falconer, (1997), “ Tidal Flow and Transport Modelling using the ULTIMATE QUICKEST Scheme”, J. Hydraulic Engineering ASCE, Vol.123, 303-314.

[2]  Kashefipour, S.M. and R.A. Falconer, (1999), “Numerical Modelling of Suspended Sediment Fluxes in Open Channel Flows”, XXVII IAHR Congress, Graz, Austria.

[3]  Kashefipour, S.M., B. Lin, E. Harris, and R.A.Falconer, (2000), “Ribble Estuary Water Quality Modelling”, Final Report, Cardiff University, UK, 454pp.

[4]  Thackston, E.L., and A.Murr (1999), “CSO Control Project Modifications Based on Water Quality Studies”, J. Environmental Engineering, ASCE, Vol.25, 979-987.

[5]  Thomann R.V. and J.A. Muller, (1987), “Principles of Surface Water Quality Modelling Control”, Harper Collins Publishers Inc., New York, 644pp.

[6]  Wyer, M.D., G. Oneill, D. Kay, J.Crowther, G. Jackson, and L.Fewtrell, (1997), “Non-Outfall Sources of Faecal Indicator Organisms Affecting the Compliance of Coastal Waters with Directive 76/160/EEC”, Water Science and Thchnology, Vol. 35, 151-156.