Nearshore wave forecasting and hindcasting by dynamical and statistical downscaling
Introduction
Coastal regions partially sheltered from the open ocean prove a difficult middle ground between open-ocean conditions and the really small scales found in harbours and the mouths of rivers and estuaries. Prognostic wave models developed for open-ocean conditions (see e.g. Hasselmann et al., 1988, Tolman, 1991) have until recently been considered too computer-intensive to be operated on grids resolving complex coastal regions (typically requiring a grid finer than 1 km).
In partially sheltered domains where local wave growth is limited and the ocean spectrum outside sheltering islands can be assumed spatially homogeneous it may be possible to use simple refraction–diffraction models O'Reilly and Guza (1993), especially if the main concern is relatively uni-directional low-frequency swell from distant storms. In such cases it may be possible to establish a tractable database (look-up table) of relations between open-ocean and nearshore conditions for various combinations of integrated parameters like significant wave height, peak direction and peak period of the wave field impinging on the boundary of the model domain. On even finer scale semi-diagnostic models designed for harbours, closed bays and estuaries (e.g. STWAVE, Smith et al., 2001) perform very well.
However, for coastal domains where local wave growth is of significance the steady-state assumption breaks down. Also, the complexity of the sea state near the open ocean with swell intrusion and young wind sea requires full two-dimensional spectra as boundary conditions to the fine-scale model. This is difficult to achieve with steady-state models because the aforementioned look-up table will grow out of bounds (the “curse of dimensionality”), making a fully non-stationary dynamical spectral wave model a computationally competitive alternative.
The advent of high-resolution prognostic wave models specifically designed to handle the high resolution needed to resolve nearshore conditions combined with numerical weather prediction models (NWP) capable of capturing the complexity of the coastal wind field opens up the possibility of forecasting the sea state in regions partly sheltered from the open ocean on spatial resolution of less than 1 km. Simulating WAves Nearshore (SWAN) is a third-generation wave model (Booij et al., 1999, Ris et al., 1999) in operational use at the Norwegian Meteorological Institute since 2006. The model is operated on 500 m resolution and is used to issue wave forecasts to the Norwegian Coastal Administration and the general public for particularly sensitive sea areas.
For this study SWAN was set up for a region on the west coast of Norway which is partially sheltered by islands to the north-west and with a larger island to the east, see Fig. 1, Fig. 2. We define a semi-sheltered coastal region as one that is exposed to wind and waves from the open ocean and is large enough for local wave growth to become important while still being sheltered by islands or mainland in other directions.
Running a high-resolution forecast system with SWAN as the wave component is computationally demanding, but tractable, in forecast mode. If detailed wind fields are also required (depending on the steepness of the topography), a detailed numerical weather prediction model must also be operated. In our case very detailed (4–5 km resolution) winds were used to force the wave model. The wind fields are taken from a high-resolution nested weather prediction system. Full two-dimensional wave spectra from a coarser wave model (WAM) are used as boundary conditions for the high-resolution model. This nested setup with full two-dimensional wave spectral information on the open boundaries will be referred to as the dynamical downscaling. Dynamical downscaling techniques for waves resemble the nesting methods employed for atmospheric and oceanographic modelling but with the important difference that the wave field is a forced dynamical system that depends solely on the wind field, the open boundary and the bathymetry. Thus, while a nested numerical weather prediction model or an ocean model would generate small-scale phenomena (eddy activity) that could not be predicted from the boundary values alone, the wave model will only respond to structures in the fine-scale wind field and details in the bathymetry that were not resolved by the coarser model.
With rapid environmental assessment (REA) in mind, the next step once a forecast system is in place will be to create annual and seasonal maps of the wave field, e.g. significant wave height and dominant wave direction. This can to a good estimate be achieved with hindcast simulations of intermediate length, typically 1 year. However, extending the high-resolution wave model integration to generate a hindcast archive covering decades is computationally prohibitive on the spatial resolution described above, at least for REA purposes. To estimate the extremes (return values) of the wave climate in coastal locations we build a direction-dependent statistical transfer function between a coarse-resolution open-ocean hindcast archive (covering the period 1955 and onwards) and the high-resolution coastal SWAN domain for the overlapping time period. This is referred to as the statistical downscaling. Local wave growth and local wind effects (land–sea breeze, funneling along the coast) as well as sheltering from nearby islands are processes in the coastal zone that can significantly alter the local wave conditions compared with the wave field in the open ocean. To account for this, our approach is to relate the offshore conditions from the coarse hindcast archive to the sea state in the coastal location found with SWAN for the common time period through a direction-dependent transfer function. A detailed study of the relative merits of statistical and dynamical downscaling of waves to nearshore conditions can be found in Gaslikova and Weisse (2006) or Gaslikova (2006). A detailed development of statistical downscaling techniques is found in Stoelinga and Warner (1999).
The objective of this study is to outline and evaluate an approach to rapid assessment of wave conditions in coastal locations with complex topography and complex sea state. We will assess a method for quickly setting up a reliable forecasting system as well as building a hindcast (climatology) series of sufficient length to properly estimate the average and the extremes of the wave climate. The method to be evaluated can be summarized as follows.
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Set up a nested high-resolution prognostic wave model capable of precisely forecasting and recreating the wave conditions in coastal, semi-sheltered waters where local wave growth and exposure to the complex open ocean wave conditions are important. Force the model with detailed wind fields if necessary (depending on the steepness of the topography and the complexity of the coastline).
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Run the model for a sufficiently long period to assess the forecast skill and to map the fine-scale spatial variations in average wave climate, i.e., the first and second moments of the wave field. This involves typically a 1-year integration.
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Use this “training” period to build a transfer function to open-ocean hindcast series and calculate extremes (return values) of the wave height distribution from the transfer function for chosen locations.
Section snippets
WAM50 and WAM10 open ocean wave models
The third-generation wave model WAM (Hasselmann et al., 1988) has been in operational use at the Norwegian Meteorological Institute since 1998. A medium-resolution (10 km) domain (hereafter referred to as WAM10) is nested in a coarse-resolution model covering the North Atlantic on 50 km grid resolution (hereafter referred to as WAM50). The model discretizes the two-dimensional spectrum with 24 directional bins and 25 logarithmically spaced frequency bins covering the range from 0.042 to 0.4 Hz.
WINCH hindcast archive
The Norwegian Meteorological Institute maintains a coarse-resolution hindcast data set covering the period 1955 and onwards. The hindcast archive is generated with a second generation wave model (WINCH, see Greenwood et al., 1985) with winds calculated in part from digitized pressure maps. The model was set up on a course (150 km to 75 km) grid which covered the northern North Atlantic, the Norwegian Sea, the Greenland Sea, the Barents Sea and the North Sea. The archive originally covered the
Assessment of method and concluding remarks
SWAN is seen to perform well on the spatial scales of interest, i.e., coastal semi-sheltered conditions with a spatial grid resolution of 500 m. The performance of the model was evaluated over two periods where buoy measurements were available (correlation 0.96) but with a bias of 0.29 m (18%). Running SWAN in forecast mode is thus a good alternative when detailed forecasts of wave conditions are required in regions where diagnostic, steady-state models prove inadequate, provided that a
Acknowledgments
This work has been supported by the Research Council of Norway and the Norwegian technology company FOBOX through project no 174104, “Development of a generic model/set of tools for prediction of waves in areas close the coast—to be used for wave energy development”. All wave buoy measurements have been normalized and all geographical references have been removed to protect the intellectual property rights of FOBOX.
We also wish to thank the two anonymous reviewers for thoughtful comments that
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