ON THE QUESTION OF THE SWAN MODEL SENSITIVITY TO CHANGES
IN TIME STEPS AND INITIAL CONDITIONS

Oleg Makarynskyy^1,2, Antonio Alberto Pires Silva², Dina Makarynska²,

Carlos Ventura Soares³ and Emanuel Ferreira Coelho³

1,2 Odessa Socio-Ecological Union, Odessa, Ukraine

Presently FCT fellow at the Instituto Superior Tecnico, Technical University of Lisbon

Av. Rovisco Pais, 1, 1049-001, Lisbon, Portugal

Tel.: +351 21 841 8343, fax: + 351 21 849 7650, E-mail: oleg@civil.ist.utl.pt

² Instituto Superior Tecnico, Technical University of Lisbon, Av. Rovisco Pais, 1, 1049-001, Lisbon, Portugal

Tel.: +351 21 841 8128, +351 21 841 8366, fax: + 351 21 8497650,

E-mail: aps@civil.ist.utl.pt, E-mail: dina@civil.ist.utl.pt

³ Hydrographic Institute, R. das Trinas, 49, 1249-093, Lisbon, Portugal

Tel.: +351 21 395 5119, fax: + 351 21 3960515, E-mail: oceanografia@hidrografico.pt

Abstract: Nearshore spectral wave modeling finds a variety of applications with increasing importance in recent years. Therefore, a study of the sensitivity of model outcome to changes of model input parameters is essential in a number of the applications.
The SWAN model was applied to a sandy beach in the west coast of Portugal. Six numerical simulations with different computational steps and initial conditions were compared to wave observations obtained with a pressure sensor deployed close to the shore.
The simulations show a low dependency of the output results to changes in the time step of computations. However, both parameters analyzed (H_s and T₀₂) depend on the initial parameterization of the wave field in nonstationary runs: the use of the hot start option allows obtaining of reliable results from the very first computational steps.

Keywords: nonstationary, numerical, simulation, spectra, conditions, nearshore

1    INTRODUCTION

The knowledge of wind waves characteristics nearshore is necessary in a variety of applications including the coastal engineering design, the safe management of coastal resources and resorts, the studies of sediment transport, coastal erosion and pollution processes.

The use of numerical modeling is essential in solution of these problems. The modeling allows calculating of wave characteristics on spatial scales ranging from the whole ocean to small basins and open harbors with different free surface, bottom and boundary conditions (Komen et al., 1994; Luo, 1995; Ris, 1997; Ventura Soares et al., 1999).

However, some permanent problems appear in carrying out of wave model experiments. For instance, Pires Silva et al. (1999) showed that the influence of zero lateral boundary conditions can be dramatic not only in the very vicinity of the boundaries but in the central areas of computational domain as well. An increasing of the reliability of model results is particularly related to the set up of the conditions based either on the data of field or preliminary numerical experiments (Pires Silva et al., 2000). Therefore, a study of the model outcome sensitivity to changes in input parameters has to be performed before any application of the results simulated.

For this purpose the SWAN (Simulation WAves Nearshore) model developed at the Delft University of Technology (Holthuijsen et al., 1993; Ris et al., 1994; Booij et al., 1996; Holthuijsen et al., 1999) was adopted. The numerical experiments were performed on a site with regular bathymetry in the west coast of Portugal. On this stage the sensitivity of the SWAN model to changing of computational steps and initial conditions was studied.

2    LOCAL MORPHOLOGY AND BOUNDARY CONDITIONS

The Pinheiro da Cruz beach is a sandy-cliff stretch located in the middle of a soft coast cell. This cell of the west coast of Portugal is an almost perfect wide-angle arch with its cord aligned with the N-S direction. It is bounded by the Sado estuary on the north and the Sines harbor on the south. North of this estuary the coastline changes its direction by almost 90º degrees. This characteristic of the coast gives some shelter from northerly waves to the referred cell. Therefore, the Pinheiro da Cruz beach is exposed to waves coming from a NW-W-SW-S sector. The bathymetry is rather regular, consisting of arches parallel to the coast with the exception of the east point of the Setubal canyon (Fig. 1). The x axis is aligned with the West-East direction and the y axis with the North-South direction.

The forcing spectra at the seaward boundary were the ones estimated at 9 a.m., 12 and 15 p.m., December 25, 1999 from the observations of a directional buoy (Sines 1D) moored in deep water (97 m depth) offshore of the Sines Harbor. These spectra represent a system with a northwestern direction of waves approaching. One of the simulated patterns of wave heights and directions is plotted in Figure 2. It is assumed that the sea state recorded in the buoy might be assigned to the open sea boundary of the domain, although the buoy is located south of the region.

3    SHORT DESCRIPTION OF THE SWAN MODEL

The SWAN model is a third generation WAM type model, suitable for the simulation of wind generated waves from the nearshore to the surf-zone, based on an Eulerian formulation of the discrete spectral wave action balance equation. Therefore, it includes all the relevant physical processes of the propagation of wind waves in shallow waters. Namely, shoaling and refraction due to bottom variations, dissipation by depth-induced wave breaking and by bottom friction.

Wave-current interactions may play an important role in some coastal areas, tidal inlets for instance, and consequently they are considered in SWAN by refraction and shoaling due to currents variations.

As a third generation wave model no a priori limitations are imposed on the spectral evolution. The non-linear wave-wave interactions (resonant quadruplets and triads) are computed explicitly by a numerical approximation. The source terms also include wind input and dissipation by whitecapping.

The major exception in the simulation of the propagation of wind waves is diffraction that is not taken into account in SWAN.

A fully implicit numerical scheme is used for the propagation in geographical and spectral space. This allows for larger time steps with small space grid intervals, which can then be chosen based just in accuracy rather than in numerical stability.

4    RESULTS AND DISCUSSION

Pires Silva et al., (2000) showed that the including an intermediate grid between the coarse and fine ones has no justification in the Pinheiro da Cruz area. Therefore, in this study one more pace was made in the direction of simplification of the computational procedure and reduction of the computational time: in the experiments discussed one computational domain was used (45000x57000 m) with a spatial resolution 200x1000 m. This resolution is high enough and coincides with the spatial step of the batymetry data in the direction of our main concern (along the x axis).

The results of six model experiments (Figures 3 and 4) were compared with observations of a pressure sensor (black solid line) deployed in 10 m depth in the Pinhero da Cruz area. The variables compared were the H_s and T₀₂. The data used for comparison were calculated in the point of the pressure sensor location.

The outcome of a nonstationary nested experiment with two domains (further mentioned as the “tested” experiment, light brown solid line in the Figures 3, 4) was included into consideration giving a notion about acceptability of the “one grid” solution and spatial resolution used in the further computations. The time step was three hours for the case.

A stationary run was performed at times indicated. This experiment is further mentioned as the “stationary” one (dark brown dashed line in the Figures 3, 4). Three numerical nonstationary experiments were carried out on the basis of the preliminary stationary run (hot start option) with different time steps of computation (20 and 30 minutes, and one hour; red solid, blue and green dashed line, correspondingly) and output (30 minutes and one hour). Finally, one additional nonstationary run was performed without the use of hot start (magenta solid line in the Figures 3, 4) aiming to check the influence of this option onto outcome results.

Different durations of model time periods in the runs are related to different computational efforts needed to accomplish the tasks. For instance, in the case of stationary run the PC time taken (Pentium II, 350 MHz, 128 Mb RAM) was about three hours for six hour period modeled. In the nonstationary nested experiment each computational step (three hours) took about one hour of the PC time. The PC time was five hours in the case of 20 minutes computational step and three hour period simulated. For both experiments with (a) 30 minutes computational step and four hour model time period and (b) one hour step and six hour period the PC time taken was about four hours.

The comparison shows no significant differences in H_s between the three nonstationary experiments with 20 and 30 min, and 1 h computational time steps and the use of “hot start” option, and simulated in the nested and stationary runs. The values of H_s in these cases are higher than ones estimated by the pressure sensor observations excepting the measurement at 11 a.m.

Differences in T₀₂ between the nonstationary experiments and stationary runs are more noticeable. All the nonstationary experiments are overestimating the values observed whereas the stationary computations show overestimated value at 9 a.m. only.

However, the nonstationary case with one hour computational step and without the use of “hot start” shows a different pattern. Both the H_s and T₀₂ parameters differ essentially as from the data of observations as from the above-described experimental results. Apparently, the SWAN model needs several computational steps to overcome the consequences of using the so-called “cold start” option.

5    CONCLUDING REMARKS

The SWAN model, suitable for the simulation of wind generated waves from the nearshore to the surf-zone, applied to the west coast of Portugal in an open beach, shows fair well agreement between the data of nearshore measurements and results of simulations.

The comparison shows no significant differences in the output results calculated in stationary runs and nonstationary experiments with four different computational time steps and the use of “hot start” option.

Meanwhile, the use of cold start in nonstationary computations gives an essentially different pattern at least on the first computational steps.

Acknowledgements

The Hydrographic Institute of the Portuguese Navy is gratefully acknowledged for making available the bathymetry and buoy data, especially Mrs M. Costa. Oleg Makarynskyy acknowledges a post-doctoral fellowship from “Foundation of Science and Technology” (SFRH/BDP/1507/2000). This work is supported by a grant from the cooperative program “The Environment and Defense” of the Ministry of Defense of Portugal and the Foundation of the Portuguese Universities.

References

[1]    Holthuijsen, L.H., Booij, N. and Ris, R.C., 1993. A spectral wave model for the coastal zone, Proc. 2^nd Intern. Symp. on Ocean Wave Measurements and Analysis, ASCE, New Orleans, USA, 630-641.

[2]    Holthuijsen, L.H., Booij, N., Ris, R.C., Haagsma, IJ.G., Kieftenburg, A.T.M.M. and Padilla-Hernandez R.., 1999. SWAN Cycle 2 version 40.01 USER MANUAL (not the short version), Delft University of Technology, Delft, The Netherlands, 117 p.

[3]    Komen, G.J., Cavaleri L., Donelan M., Hasselmann K., Hasselmann S., Janssen P.A.E.M., 1994. Dynamics and modelling of ocean waves. Cambridge University Press, 532 p.

[3]    Luo, W., 1995. Wind wave modelling in shallow water, (Ph.D. Dissertation, Katolieke Universiteit Leuven), Heverlee, Belgium, 200p.

[4]    Pires Silva, A.A., Makarynskyy, O., Ventura Soares, C. and Coelho, E., 1999. Propagation of the wind waves onto the Pinheiro da Cruz open beach: application of the SWAN model, Actas 1º Jorn. Port. de Engng. Costeira e Portunia., 15-16 November 1999, PIANC-DP, Porto, Portugal. 47-58. (in Portuguese)

[5]    Pires Silva, A.A., Makarynskyy, O., Monbaliu, J., Ventura Soares, C. and Coelho, E., 2000. Modeling wave transformation in an open beach on the west coast of Portugal. Coastal Waves Meeting. Book of Abstracts, A.Sanchez-Arcilla, S.Ponce de Leon (eds.), Technical University of Catalonia, Barcelona, Spain. 4.3.

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[8]    Ventura Soares, C., Coelho, E., Pires Silva, A.A. and Makarynskyy, O., 1999. PAMMELA: prediction of the wind waves on the shallow water, Actas 1º Jorn. Port. de Engng. Costeira e Portunia., 15 – 16 November 1999, PIANC-DP, Porto, Portugal. 59-70. (in Portuguese)

Fig. 1    Bathymetry of the Pinhero da Cruz.area, Portuguese Military System of Coordinates. Red lines-isolines of depths in 50m

Fig. 2    Spatial variations of H_S with scale of colors and directions of waves (lenghts of vectors are proporcional to the value on the open boundary) for 12 p.m., December 25, 1999

Fig. 3    Comparison of H_S between measurements (pressure sensor) and simulations

Fig. 4    Comparison of T₀₂ between measurements (pressure sensor) and simulations