Downscaling wave energy resources to coastal areas
Paula Camus, Antonio Tomas, Cesar Vidal, Fernando J. Mendez, Raul Medina, Inigo J .Losada.
Environmental Hydraulics Institute IH Cantabria, Universidad de Cantabria
Avda. Los Castros, s/n. Santander, 39003SPAIN
[email protected]
Abstract-Ocean wave reanalysis databases need to be downscaled to increase the spatial resolution and simulate the wave
transformation process in order to obtain wave energy resources in shallow waters. A hybrid downscaling methodology to transfer
wave energy resources to coastal areas is proposed combining a numerical wave model (dynamical downscaling) with mathematical
tools (statistical downscaling). A maximum dissimilarity selection algorithm (MDA) is applied in order to obtain a representative subset
of wave and wind conditions in deep water areas. These selected situations are propagated using a state-of-the-art wave propagation
model. The time series of the propagated wave power at a particular location are reconstructed using a non-linear interpolation
technique based on radial basis functions (RBFs), providing excellent results in a high dimensional space with scattered data as occurs
in the cases selected with MDA. The validation of the results using buoy data confirms the ability of the developed methodology to
reconstruct wave energy resources in shallow water at a particular location and to estimate spatial wave power with a considerable
reduction in the computational effort.
I.
INTRODUCTION
World wide wave energy resources can be assessed using satellite data or long-term wave reanalysis data bases from numerical
models with enough spatial (say 0.1 to 1º) and temporal resolution (more than 20 years of hourly sea states). However, coastal
wave energy resources require a more detailed spatial resolution (say, 100 m) including wave transformation process in shallow
waters. This specific problem of dynamical downscaling, enhancing the spatial resolution and defining in detail shallow water
areas, is called “wave propagation” and requires numerical models that consider the wave propagation processes such as
refraction, shoaling, diffraction and dissipation by wave breaking. A high computational effort is required to dynamically
downscale the large-scale information from reanalysis databases. In this work, we present a hybrid methodology which combines
statistical downscaling (mathematical tools) and dynamical downscaling (numerical wave model) in order to reduce the
computational time effort [1].
II.
METHODOLOGY
The steps of the methodology (shown in the Figure 1) are:
(a) definition of wave climate in deep water from historical
calibrated reanalysis databases; (b) selection of a
representative subset of open water conditions (defined by the
wave boundary conditions and wind field in the nested
computational grid of the numerical model) using a maximum
dissimilarity selection algorithm (MDA); (c) deep water-toshallow water wave transformation of these selected cases by
means of a wave propagation model; (d) reconstruction of the
time series in shallow water using a non-linear interpolation
technique based on radial basis functions (RBFs); (e)
validation of the results using instrumental data; (f)
characterization of wave energy resources at shallow waters
using different statistical models.
Reanalysis wave
database
Satellite and deep
water buoy data
Calibration
Selection
Propagation
Bathymetry
and sea
level data
Time series
reconstruction
Wave data from
coastal buoys
Validation
Coastal wave energy
resources characterization
Fig. 1 IH Cantabria framework to characterize wave energy
resource in coastal areas.
III.
DATABASES
The Global Ocean Wave 1.0 (GOW 1.0) database has been used to define the open wave conditions. This hourly reanalysis has
been developed by IH Cantabria using WaveWatch [2] and is forced with the NCEP/NCAR [3] atmospheric reanalysis (validated
with satellite data by IH Cantabria), with a temporal coverage spanning 61 years (1948-2008), an hourly resolution and a spatial
resolution of 1ºx1.5º at a global scale. The data is generated with a resolution of 0.5ºx0.5º (the GOW Iberia grid) and with a
978-1-61284-4577-0088-0/11/$26.00 ©2011 IEEE
resolution of 0.1ºx0.1º near the coast (the GOW Cantabrico grid), see figure 2. This database provides spectral sea state
parameters: significant wave height (Hs), mean period (Tm), peak period (Tp) and mean direction (θm) as well as the directional
spectra components S(f,θ), along the coast.
The GOW reanalysis data is propagated to shallow waters by nesting a numerical model which simulates the wave
transformation processes in shallow waters in order to define the wave energy resources near the coast. The proposed
methodology was then applied to the west coast of Spain (Figure 2) considering a downscaling grid with a spatial resolution of
0.01º x 0.008º. The instrumental data located in the study area are the Villano buoy (located in deep water) and the Coruña and
Langosteira buoys (in shallow water), belonging to Puertos del Estado. This valuable information is used to validate the proposed
methodology.
Fig. 2 IH GOW 1.0, Iberia and Cantabrico grids, NCEP/NCAR grid of the wind reanalysis database.
The proposed downscaling grid in the area of study and the instrumental data available.
IV. CALIBRATION
The wave data are calibrated using satellite and deep water directional buoys data from the Spanish wave measurement
network (Puertos del Estado, Spain) located in the node’s surroundings (1.5º radius area). A directional calibration is carried out
by fitting the parameters of a potential function that relates the wave instrumental data to the simultaneous reanalysis data for
each directional bin [4]. The left panel of Figure 3 shows an example of the satellite data points used in the calibration of one
node of the GOW reanalysis database in the study area. The middle panel of Figure 3 shows the calibration coefficients of the
same GOW point in the Cantabrian Sea and the right panel shows the improvement of the quantiles of significant wave height
after the calibration.
Fig. 3 Satellite wave data points used for calibration of reanalysis wave data in one GOW points in the area of study.
Calibration rose for Hs obtained for this GOW point. Quantiles of Hs before (blue) and after (red) the calibration.
V. SELECTION
The wave boundaries of the propagation model are defined from the nodes of the Cantabrico grid of the GOW database with a
spatial resolution of 0.1º. The corresponding wind fields are defined from the NCEP/NCAR database, with a spatial resolution of
1.9º and a 6-hourly temporal resolution, in order to consider the local sea wave generation.
The time series of the wave boundary conditions and the wind fields in the case study, which are going to be used in the
selection and interpolation processes, are defined by the sea state parameters Hs, Tm, θm of 11 points located at the grid boundaries
and the wind conditions Wx,Wy of 8 points located at sea from NCEP/NCAR fields (see Figure 4, blue arrows represent the wave
boundary condition of the downscaling grid and the green arrows the wind conditions).
Figure 4: Time series of the computational conditions (wave data along the grid boundaries of the wave propagation model
and wind data from the NCEP/NCAR database).
The aim of the selection process is to extract a subset of wave and wind situations representative of open-water conditions.
Therefore, the maximum dissimilarity algorithm (MDA) [5] is applied to these time series to obtain a subset of size M
representative of the deep-water wave climate diversity [1]. The data dimension is reduced by Principal Component Analysis
(PCA) to extract as much correlation as possible from spatial fields while maintaining the data variability in order to simplify the
selection process. The MDA algorithm is applied in the reduced space (defined by Principal Components, PCs). Once the M
subset is selected, the cases are identified in the original space. Figure 5 shows the catalog of M=500 MDA selected cases in the
study area.
Figure 5: M=500 grid boundary selected by MDA
VI. PROPAGATION
The M=500 selected cases by MDA, representative of the wave climate at deep water, are propagated to coastal areas using the
wave numerical model SWAN [6]. These cases are defined by the wave boundaries at the downscaling grid with a resolution of
0.01º x 0.008º (defined by directional spectra every 0.1º node) and the corresponding wind fields (defined by 12 nodes of the
NCEP/NCAR reanalysis database). The wave energy parameters at the nodes of the downscaling grids are obtained for each case
(j): the propagated wave power (Pwp,j), and the mean wave energy direction (θEp,j).
The subset of the M=500 propagations in the downscaling domains defined a library (catalog) of cases formed by the M=500
hourly sea state parameters (Pwp, θEp), corresponding to specific deep water wave climate conditions. The catalog of the M=500
situations for the wave energy parameter Pw (kW/m) and θE is represented in Figure 6.
Figure 6: Library with M=500 propagations. Wave power Pw (kW/m) and energy direction θE
VII. RECONSTRUCTION OF TIME SERIES
The time series of each propagated parameter {Pwp, θEp} is reconstructed by a multilinear interpolation technique based on
radial basis functions (RBF). The approximation function of each parameter is formed by a lineal combination of radial basic
functions centered on the scattered points defined by the MDA cases in the PCA space, with the associated real function values
which are the corresponding propagated parameters. In this work, a Gaussian function has been used in the interpolation
technique and the optimal shape parameter has been obtained by Rippa’s algorithm [7] based on a leave-one-out cross validation.
VIII.
VALIDATION
The reconstructed time series of the wave energy at the location of the buoys Villano, Coruña and Langosteira (belonging to
Puertos del Estado) are shown in the left panels of Figure 7 and they are compared to the instrumental data. In the right panel, the
scatter diagrams of the wave energy parameter (Pw, units: kW/m) are shown. The numerical validation of the results confirms the
ability of the developed methodology to reconstruct wave energy time series in shallow water at a particular location with a
considerable reduction in the computational effort.
Figure 7: Validation of the time series reconstruction of wave power at the available buoys
Figure 8 shows the validation of the wave power statistics at the directional buoys of Villano (at deep water) and Langosteira
buoy (coastal buoy). The upper panels show the aggregated time series of mean power (the monthly mean power, the annual
mean power and the mean direction of monthly power and the mean direction of the annual power direction). Finally, the lower
panels represent the seasonal mean power with the mean power and the directional distribution of mean power. As can be seen,
the proposed methodology is able to reproduce the temporal structure of wave climate and the directional distribution of wave
energy.
Figure 8: Validation of the annual and seasonal wave energy resources and the directional distribution at the available
directional buoys (Villano and Langosteira). Units: kW/m.
IX. RESULTS- SPATIAL WAVE ENERGY RESOURCES STATISTICS
The subset of the M propagated cases selected by MDA algorithm defines a library of M hourly wave energy parameters: wave
power (Pwp), and mean wave energy direction (θEp) at the nodes of the computational grid, corresponding to the associated deep
water conditions. Although MDA algorithm is not a clustering technique, we can consider that each data is represented by the
closest vector of the selected subset [1]. Therefore, each selected case has an associated probability, which is a function of the
number of similar deep water conditions represented by each one. An easy spatial definition of wave climate statistics is possible
by means of the results of the propagation of the M cases and the corresponding probability without applying the most time
consuming RBF interpolation scheme.
Therefore, the wave resources can be also be spatially characterized. Figure 9 shows the mean wave power (upper left panel),
the 95th annual percentile of wave power (upper right panel), the winter mean wave power (lower left panel) and the summer
wave power (lower right panel), revealing a strong spatial variability, especially nearshore, and seasonal variability of wave
energy resources.
Figure 9: Spatial wave energy resources in the area of study: a) annual mean wave power; b) the 95% percentile of wave power;
c) the wave power at winter (DEF); d) the mean wave power at summer (JJA). Units: kW/m
X. CONCLUSIONS
A hybrid methodology to downscale wave energy resources increasing the spatial resolution has been proposed. The
methodology is based on a selection of M situations representative of wave boundary conditions and deep water wind fields by
MDA, the dynamical propagation of these selected cases and a multidimensional RBF interpolation to reconstruct the time series
of shallow water wave parameters.
The proposed methodology has been applied to an area around the west coast of Spain. The validation of results confirms that
the proposed methodology is able to reproduce the time series of wave power at coastal areas. The good performance of the
methodology is due to the adequate sampling of the variability of open-water wave and wind conditions using MDA selection,
not only for the representativeness but also for the convenience to the subsequent application of the interpolation scheme. The
RBF technique, improved by the Rippa algorithm [7], has proved to be a powerful technique to reconstruct hourly time series of
wave power. Furthermore, the library of M propagations with its corresponding probabilities supposes an efficient and easy
method to estimate high resolution of spatial wave climate statistics.
ACKNOWLEDGMENTS
The authors are grateful to the funding provided by projects “GRACCIE” (CSD2007-00067, CONSOLIDER-INGENIO 2010)
from the Spanish Ministry of Science and Technology, “MARUCA” (200800050084091) from the Spanish Ministry of Public
Works, “C3E” (E17/08) from the Spanish Ministry of Environment, Rural. A special thanks to “Puertos del Estado” for providing
the information from the instrumental data base.
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