Application of a Two-dimensional Hydrodynamic Model for Shallow Waters to the Orbetello Lagoon S. Marsili-Libelli (*), G. Pacini, P. Covelli Department of Systems and Computers, University of Florence, Via S. Marta, 3 – 50139 Firenze, ITALY (*) Email:
[email protected] Abstract An integrated hydrodynamic and water quality package is demonstrated with its application to the Orbetello lagoon. Through simulations it is shown that natural circulation in the lagoon is insufficient to guarantee enough water exchange for a viable ecological equilibrium. The inadequacy of the present artificial pumping scheme is also shown. This tool is going to be integrated in the decision support system designed to manage the lagoon ecosystem. Keywords Decision support systems, hydrodynamic modelling, software engineering.
Introduction Shallow water bodies constitute environmentally sensitive areas and their management is becoming increasingly complex, requiring an interdisciplinary approach encompassing ecology and hydrodynamics as well as socio-economic and computer disciplines. This paper presents the application of a self-contained interactive hydrodynamic and water quality modelling environment especially conceived for shallow water bodies, named SWAMP (an acronym for Shallow Water Analysis and Modelling Program) to a salt-water lagoon along the coast of the Tyrrhenian sea, in central Italy. The aim of this paper is to describe the application of SWAMP to the study of water movements in the Orbetello lagoon. Though the authors are too well aware that a number of more sophisticated tools already exist for hydraulic modelling, it is still considered worthwhile to produce a self-contained stand-alone package with good interactive capabilities and an emphasis on integration between the hydrodynamic and water quality modules. In this light, the quality of the software should be assessed not only in terms of computational performance, but also with regard to interface efficiency and seamless integration among the different modules. The Orbetello lagoon The Orbetello lagoon has an extension of about 27 km2. Figure 1 shows that in the past (Figure 1 left) both lagoons were in fact a single cove with ample seawater circulation. Now the lagoon is composed of two enclosed coastal ponds. In the west bank there are two inlets through which sea water can be pumped in (arrows n. 1 and 2 in Figure 1 right), and one outlet in the east bank (n. 3) from which water is pumped out of the lagoon. The two ponds communicate though a narrow passage (4) under a bridge connecting Orbetello with Mount Argentario. Natural water flow through these inlets, induced by tide and wind, is insufficient Hydroinformatics 2002: Proceedings of the Fifth International Conference on Hydroinformatics, Cardiff, UK © IWA Publishing and the authors. ISBN 1 84339 021 3 (set)
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to provide the necessary turnover, hence the need to resort to forced pumping, which normally has the direction indicated by the arrows, but can also be reversed. In the last few years, nutrient build-up and insufficient water movement has resulted in eutrophication and a general deterioration of water quality. The study presented in this paper is part of a project to control eutrophication through water movement and macroalgae collection, in order to prevent major environmental damages. While the recognition of water conditions favourable to macroalgal bloom are described elsewhere (Marsili-Libelli et al., 2002), this paper will present the adaptation of SWAMP to describe the water movements resulting from a combination of natural forces (wind and tide) and artificial control actions (pumping).
Figure 1 The Orbetello lagoon, in circa 1750 (left) and now (right).
The SWAMP Package The features of the SWAMP package, which are thoroughly described elsewhere (Covelli et al., 2002) will be summarised first, then its application to the hydrologic situation of the Orbetello lagoon will be considered, assessing the system sensitivity to the various inputs, either natural or artificial.
The SWAMP package This software package, named Shallow Water Analysis and Modelling Program (SWAMP), was developed in Matlab specifically for shallow water bodies with slow circulation. In fact this configuration requires special techniques to define the velocity field in an accurate way (Wang and Falconer, 1998). Generally, after the hydrodynamic computation the problem arises of exporting the velocity field into a water quality model and then to integrate the results into a decision support system. Separate modules are generally invoked for this, resulting in a complex, poorly flexible system. Commercially available packages (e.g. MIKE21, DHI, Denmark) are often too expensive to be affordable by local administrations and require a large amount of data, together with special expertise, to fully justify their cost. The solution presented in this paper advocates the joint development of the hydrodynamic,
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water quality modules and graphical user interface into a single application. The resulting software can then be integrated in a decision support system. For space reasons, the numerical treatment of the Shallow Water Equations (SWE) and the linkage between the hydrodynamic and water quality modules cannot be reported here, but they are thoroughly explained elsewhere (Covelli et al., 2002). An explicit centered finite difference scheme has been used to solve the full SWE. This method is based on that originally proposed by Iwasa and Inoue (1982) and has been adapted for modelling hydraulic flow in shallow water bodies. This scheme operates on a C-shaped region using a centeredtime/centered-space strategy. The horizontal two-dimensional advective-diffusion equation solution algorithm is derived from the Mac Cormack predictor-corrector scheme (Mac Cormack, 1969). The predictor-corrector method operates on a water quality grid consistent with that of the hydrodynamic module. In this context, the software engineering aspect will be described while being applied to the Orbetello lagoon. SWAMP software engineering SWAMP has been developed in the MatLab® 5.3 platform, which provides the backbone of the graphical user interface, whereas the computational engine is coded in C++® and linked as Dynamic Linked Library (DLL) to the main Matlab program. The SWAMP structure is shown in Figure 2. Morphology Hydraulic parameters Grid parameters Boundary conditions
Initial conditions Simulation parameters
Visual C++ DLL Pre-Processing Pre-Processing
Main Program Main Program Parameters input
Parameters input Monitoring points definition Monitoring points definition Input files generation Input files generation Simulation initialisation Simulation initialisation
Input files
Numerical Numerical Solution Solution Algorithm Algorithm Output files
archive Post-Processing Post-Processing archive
Matlab
space space
time time
Figure 2 Software engineering structure of SWAMP.
This architecture presents a simple front-end to the user, while maintaining the flexibility of an open framework. The C++® subroutines, implementing the core of the hydrodynamic, water quality and numerical integration modules, is wholly transparent to the user. At the same time, the MatLab® main program allows easy handling of the user interface and inputoutput data exchange. The most important tasks, apart from the computational engine, are the pre- and post-processing modules, which will now be described with the aid of the Orbetello application.
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SWAMP application to the Orbetello lagoon The steps necessary to set-up and run an hydrodynamic simulation with SWAMP are now described with reference to the Orbetello case study. The pre-processing module allows the reconstruction of the basin trough a threedimensional interpolation algorithm starting from morphological data. The digital terrain model (DTM) is then transformed into a user-defined constant-step rectangular grid. During this procedure all hydrodynamic parameters can be defined on a node-by-node basis to consider the effect of different roughness of the bottom. In the Orbetello case this is important to account for zones with different, often competing, vegetation, e.g. seagrass vs. seaweed. The latter, being rooted to the bottom, produces a much larger drag than the former. The typical pre-processing steps are: Step 1 - Topographic data can be acquired directly as numerical data (ASCII, DTM format) or entered directly through a digitiser (Figure 3). The morphological data are stored as single points in three-dimensional co-ordinates Pn(xn,yn,zn);
Figure 3 Direct digitalisation of terrain depth curves.
Figure 4 Generating the rectangular integration grid.
Step 2 - Single spatial points are interpolated to produce the integration grid, based on Delaunay triangulation which can be performed in a cubic, linear or nearest mode; Step 3 - A rectangular mesh is generated dynamically adjusting spatial discretization in the x and y directions. The user can specify a suitable grid size so that computational effort and accuracy are well balanced (Figure 4). The total number of elements is minimised by ignoring areas without morphological data;
Figure 5 Definition of hydraulic roughness Figure 6 The final appearance of the basin, coefficient for each cell. once an initial water elevation and inlet and outlet points are defined.
Step 4– Defines the hydraulic characterisation of the domain, assigning an individual roughness coefficient to each node (Figure 5) so that the local hydrodynamic friction due to submerged macrophytes or bottom structures can be accounted for. Boundary water flows and initial water level are also defined by the user in this step;
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Step 5 - The input file containing all the information required to perform a simulation is generated and saved (Figure 6). Now the problem is completely defined and hydrodynamic simulations can be performed. All the information required for the simulation are controlled by the main SWAMP window in which forcing functions, e.g. input mass and wind conditions can be defined together with time-step size, compatible with the time-space step constraint. The simulation results are managed by the post-processing module, which can display vector or three-dimensional representation of the hydrodynamic flux.
Water movement simulation Several simulations are now shown to demonstrate the package and assess some important characteristics of the Orbetello lagoon. Figures 7 and 8 consider a natural situation, without artificial pumping. The water movement are mainly induced by the wind, whereas the tide has a negligible effect. In fact tidal level changes never exceed 25 cm out at sea. Given the head loss through the pumping channels, this variation is almost entirely damped before entering the lagoon. This situation is shown in Figure 7 where some water velocity gradient is discernible only around the channels and through the road bridge, with the rest of the lagoon being unaffected. By contrast, Figure 8 shows a simulation with the prevailing southwesterly wind of average speed (7 m/s). It can be seen that the wind affects the whole lagoon surface and is capable of inducing some local water movements. Still, this does not imply water exchange with the sea. In fact most water movement is confined within the lagoon, given the hydraulic resistance of the inlets and related pumping installations.
Figure 7 SWAMP simulation of the water circulation at low-tide with no wind (the picture is turned 90° anticlockwise).
Figure 8 SWAMP simulation of the water circulation at low-tide with a 7 m/s SW wind (the picture is turned 90° anticlockwise).
Lastly, Figure 9 shows the effect of a typical pumping scheme, with flows of 1 m3/s and 3 m /s from the west inlets and water withdrawal at the same rate (4 m3/s) from the east outlet. The limited effect of this policy is clearly shown, producing only small local velocity gradient around the ports and leaving the bulk of the lagoon unaffected. As a result of this 3
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simulation study, the effectiveness of the present pumping configuration is being questioned and alternatives, such as widening the ports, are being considered. 3 m/s
1 m/s 4 m/s
Figure 9 Flow velocity distribution with artificial pumping into the lagoon from the west ports and water extraction through the east port.
Conclusion This paper has presented the application of a self-contained hydrodynamic and water quality package (SWAMP), specifically conceived for shallow water modelling, to the Orbetello lagoon where a control strategy of the pumping station has to be designed to enhance the water movement. Through SWAMP simulations the effect of natural agents, wind and tide, is proved insufficient and a new, more suitable combination of pumping at the three sea-ports is now being sought for.
Acknowledgement This research is supported by the Committee for the Management of the Environmental Emergency in the Orbetello Lagoon, under the supervision of the Tuscany Regional Government.
References Covelli P., Marsili-Libelli S., Pacini G. (2002). SWAMP: A two-dimensional hydrodynamic and quality modelling platform for shallow waters. Numerical Methods in Partial Differential Equations (to appear in the July 2002 issue). Iwasa Y. and Inoue K. (1982). Mathematical simulations of channel and overland flood flows in view of flood disaster engineering. Journal of Natural Disaster Science, 4 (1), 1-30. Mac Cormack R.W. (1969). The effect of viscosity in hypervelocity impact cratering. Am. Inst. Aeronaut. and Astronaut. , Paper. 69-354 , New York. Marsili-Libelli S, Pacini G., Barresi C. (2002) Fuzzy Prediction of the Algal Blooms in the Orbetello Lagoon, Proc. 1st Biennial meeting of the International Environmental Modelling and Software Society, Lugano (CH), 24 - 27 June. Wang H. and Falconer R.A. (1998). Simulating disinfection processes in chlorine contact tanks using various turbulence models and high-order accurate differences schemes. Water Research, 32 (5), 1529-1543.
