Long-term hindcast for Wave Hub,
Cornwall
Validation and analysis of modelled results
J. van Nieuwkoop-McCall, H. Smith, Prof. G. Smith, L. Johanning
University of Exeter
March 2012
Conducted for the TSB project: ‘Accelerated Development of the PB500 for
Deployment at Wave Hub’
Hindcast Wave Hub
Table of Contents
1
2
3
4
5
Introduction .................................................................................................................................... 3
1.1
Problem description................................................................................................................ 3
1.2
Project objectives.................................................................................................................... 3
Wave model .................................................................................................................................... 4
2.1
Introduction ............................................................................................................................ 4
2.2
Model description ................................................................................................................... 4
2.3
Model set-up ........................................................................................................................... 4
Validation with buoy data ............................................................................................................... 7
3.1
Introduction ............................................................................................................................ 7
3.2
Buoy data ................................................................................................................................ 7
3.3
Validation of hindcast data ..................................................................................................... 7
Wave resources............................................................................................................................. 17
4.1
Method ................................................................................................................................. 17
4.2
Data analysis location 1 ........................................................................................................ 19
4.3
Spatial variation in Wave Hub area....................................................................................... 30
Conclusions ................................................................................................................................... 34
Literature .............................................................................................................................................. 36
Appendix A Analysis corrected hindcast data ....................................................................................... 37
Appendix B Relation to previous studies .............................................................................................. 42
Appendix C Directional variation .......................................................................................................... 44
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1 Introduction
1.1 Problem description
There are numerous measured and modelled datasets available within 20 km of the Wave Hub site
covering different periods between 1989 and 2012. However, there is no single dataset covering the
entire period and the measured datasets cover short periods of up to a year, consequently there is
limited temporal overlap of the datasets. The different instruments and models used to produce
each dataset, and the natural inter-annual variability of the site, make the assessment of wave
resources and extreme wave heights more difficult and less reliable.
Additionally, the datasets available cover a significant area, with differing bathymetry, so a variation
in wave climate is to be expected. Due to change in the site location during development there is
only one measured dataset at the final Wave Hub development area and no information about the
variation inside this area.
1.2 Project objectives
Reanalysis wave and wind information from large scale ocean models has been used as input for a
high resolution regional SWAN model. In this way, a dataset for the Wave Hub development area
with a 23-year period and more spatial information is created.
The objective of this report is to present the analysis of this dataset. This entails:
• To present the validation of this dataset against buoy data;
• To present a wave resource assessment for the Wave Hub development area;
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2 Wave model
2.1 Introduction
This chapter describes the SWAN model that was used for the 23 year hindcast. First a description of
the model physics is given in section 2.2. Subsequently, various model choices are discussed in
section 2.3. Detailed information about the model set-up can be found in ‘A Wave model for the
Cornwall coast’, August 2011.
2.2 Model description
The spectral wave model SWAN (Booij et al. 1999) is used for the hindcast of the wave conditions
over a 23 year period. The third generation mode for wind input, quadruplet interactions and
whitecapping is used. SWAN computes the evolution of wave action density N using the action
balance equation:
With
The terms on the left-hand side of equation 1 represent, respectively, the change in wave action
over time, the propagation of wave action in geographical space, depth and current-induced
refraction (with propagation velocity cθ in directional space θ) and the shifting of the relative radian
frequency σ due to variations in mean current and depth (with the propagation velocity cσ). The
right-hand side of equation 1 represents processes that generate, dissipate or redistribute wave
energy, given by equation 2. These include the deep water processes of wind input (Sin),
whitecapping dissipation (Swc), quadruplet nonlinear interaction (Snl4), and the shallow water
processes of bottom friction dissipation (Sbot), depth-induced breaking (Sbr) and triad wave-wave
interactions (Snl3).
SWAN default parameterizations for wind, nonlinear quadruplet wave interactions, bottom friction
dissipation, depth-induced breaking and triad wave-wave interactions are used. For whitecapping
the formulation proposed by Rogers (Rogers 2003) is used. The weighting of the relative
wavenumber term in the whitecapping formulation is altered (n = 2 instead of n = 1). By increasing n,
the dissipation is reduced at lower frequencies and increased at higher frequencies compared to the
default SWAN settings.
2.3 Model set-up
The model covers the area of 4 to 7 degrees west and 49 to 51 degrees north. The model grid
comprises the whole Cornwall coast and part of the Devon coast. Furthermore, the Isles of Scilly are
included. A grid resolution of 1 km x 1 km is used for the model domain. Nests with smaller grid
resolutions, down to 100 m x 100 m are used for nearshore areas of interest. The nest for the Wave
Hub area is shown in figure 2.1. The nests for the area around Falmouth and for the Isles of Scilly are
not shown in this figure.
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The bathymetry for the model is constructed from the bathymetry obtained from Marine DigiMap.
Figure 2.1 shows the bathymetry in a selection of the model domain.
Output is generated at various points along the model grid. The output points relevant to this study
are shown in figure 2.1. The green squares indicate the validation points for validation against buoy
data. Furthermore, various integral parameters are written to an output file for the entire Wave Hub
area. For one point in this area spectral information is also given.
PRIMaRE buoys
Wave Hub
Nest Wave Hub
Perranporth
Looe Bay
Penzance
Porthleven
Figure 2.1: Bathymetry and output locations
The global model hindcast of ECMWF (European Centre for Medium-Range Weather Forecasting),
utilising the wave model WAM, provides the wave and wind input. The grid resolution of this model
is 1.5 x 1.5 degrees and is therefore very coarse compared to the SWAN model resolution, see figure
2.2. The time resolution of the ECMWF global model is 6 hours. ECMWF provides the integral wave
parameters Hm0, Tp, wave direction and wind velocity and wind direction. The wave parameters were
interpolated to the SWAN model corner points using a matlab routine. The ECMWF wind data was
interpolated to the SWAN model grid by SWAN itself. No water level variations and currents are
taken into account.
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th
Figure 2.2: ECMWF model grid and every 10 grid line of the SWAN grid (black dots), wave boundary input points (red
circles)
The period between 1 January 1989 to 1 November 2011 is hindcasted with a time step of 60
minutes. The spectral direction covers the full circle and a bin of 8° is chosen for the SWAN
computations to provide a sufficiently fine resolution for swell waves. For the spectral resolution a
range from 0.03 – 0.6 Hz is used, which results in 31 bins.
SWAN version 40.81 has been used for the model computations. Use was made of a Beowulf cluster
with 512 nodes. The hindcast has been split into periods of 2.5 years and was run in a period of 2
weeks.
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3 Validation with buoy data
3.1 Introduction
In this chapter the modelled wave data for specific sites are validated against buoy measurements.
In section 3.2 an overview of the available measurements is given. In section 3.3 the validation
against the buoy data is presented in various ways and error correlations with different integral
parameters are analysed.
3.2 Buoy data
The model set-up has been validated against buoy data from 6 different buoys over the time periods
where data is available. The buoys include two of the PRIMaRE wave buoys situated near the Wave
Hub and four Coastal Channel Observatory buoys: Perranporth, Penzance, Porthleven and Looe Bay,
see figure 2.1.
Prior to using any of the buoy measurements, each dataset was processed and subjected to a basic
quality control test to ascertain the validity and reliability of the data. First outliers and data outside
the physically realistic limits were removed. Subsequently, the wave parameters were averaged
using a 3 hour moving average. The 3 hour time window was chosen to consistently compare data
against the model outputs, corresponding to the temporal resolution of wind forcing and wave
boundary input. Finally the data were interpolated on regularly spaced time vectors in order to be
able to compare them with the modelled data.
Table 3.1 gives details on location, depth and measurement periods for all buoy locations.
Table 3.3.1: Wave buoy location details
buoy name
PRIMaRE A
PRIMaRE D
Perranporth
Penzance
Porthleven
Looe Bay
location
5.67°W;50.31°N
5.67°W;50.31°N
5.18°W;50.35°N
5.50°W;50.11°N
5.31°W;50.06°N
4.41°W;50.34°N
depth
37m
37m
15m
10m
12m
12m
period
02/2010-11/2010
10/2009-11/2010
11/2006-10/2011
03/2007-10/2011
10/2011-10/2011
05/2009-10/2011
08/2011-10/2011
08/2011-10/2011
3.3 Validation of hindcast data
Statistical comparison
The statistical results of the comparison between the measurement data and model results are
shown in table 3.2. For each dataset the bias, the relative bias, the root mean square error (RMSE)
and the scatter index (SI, which is the root mean square error normalized by the mean of observed
values) have been calculated.
It can be seen that the significant wave height is generally underestimated by a few centimetres by
SWAN. Comparisons between model and measurement data reveal a root mean square error in the
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order of 0.3 m. This means that the scatter index is approximately 20% for the northerly locations.
Penzance and Looe Bay have a relatively high scatter index due to the fact that average wave height
is lower at these locations. These buoys are relatively close to the shore and in shallow water and
therefore errors are more likely because of wind input errors on the land-sea boundary, shallow
water processes and wave-current interactions.
The wave period is also underestimated. In general, less underestimation of the wave period can be
seen for south coast locations than for north coast locations. The scatter index varies between 20
and 30% depending on the location.
Table 3.3.2: Wave buoy validation statistics
buoy name
N
Bias
PRIMaRE A
PRIMaRE D
Perranporth
Penzance
Porthleven
Looe Bay
5006
7050
40003
38562
363
19159
-0.08m
-0.05m
-0.06m
-0.09m
-0.01m
0.05m
Hm0
R. bias
RMSE
SI
-4%
-3%
-4%
-15%
-1%
6%
0.29m
0.32m
0.28m
0.19m
0.27m
0.20m
17%
17%
19%
32%
19%
24%
N
5006
7050
40003
38562
363
19159
bias
-1.4s
-1.2s
-1.6s
-1.1s
-0.5s
-0.5s
Tm-1,0
R. bias
RMSE
-18%
-15%
-20%
-17%
-7%
-9%
1.9s
1.6s
2.2s
2.2s
1.0s
1.7s
SI
24%
20%
27%
35%
13%
28%
Timeseries
Figures 3.1 and 3.2 show the comparison between the measured and computed datasets for
PRIMaRE wave buoy D and Looe Bay. The figures illustrate that the performance of the model
compared to the measurements is best for medium range wave heights between 0.5 and 3 meters.
Above and below these levels the wave height is often underestimated by the model.
It can be seen that the wave period is almost consistently underestimated by the model at the
PRIMaRE wave buoy D. The correspondence between measured and computed wave period is
better for Looe Bay. The computed wave direction compares in general relatively well to the
measurements for both locations.
In addition, the lower two panels in figure 3.2 show the wind direction and velocity input compared
to measured wind at the Looe Bay wave buoy. It can be seen that the ECMWF wind has a very
smooth line, whereas the measured wind is very erratic. Moreover, the peaks in wind velocity are
often underestimated by the ECMWF data whereas the lower wind velocities are often
overestimated. An error in the wind field has large consequences for the computed significant wave
height, as the wave height is strongly correlated to the wind speed.
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Figure 3.1: Timeseries comparison of computed and measured data PRIMaRE wave buoy D
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Figure 3.2: Timeseries comparison of computed and measured data Looe Bay
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Error dependence on wave height and period
By looking at the error in more detail dependencies between the error and some parameters can be
found. Figures 3.3 to 3.6 present the bias and root mean square error of Hm0 and Tm-1,0 binned by Hm0
and Tm-1,0. The number of observations in each bin is shown in figure 3.7.
Figure 3.3 shows that the largest negative bias (larger than 0.5 meters) occurs either for very steep
waves or long waves. The largest positive bias occurs for long waves with wave heights smaller than
1 meter. The smallest bias can be found for wave heights between 0 and 3 meters and wave periods
between 4 and 10 seconds. The probability of occurrence in this range is also the highest, see figure
3.7. The root mean square error, shown in figure 3.4, demonstrates the same trend as for the bias.
All bias on Tm-1,0 is negative, see figure 3.5. A clear correlation can be seen between the bias and the
steepness of the waves. The smallest bias is found for the steeper waves, whereas the largest bias
(circa 5 seconds) can be found for long small waves. The root mean square error, shown in figure
3.6, demonstrates a similar trend as the bias.
Figure 3.3: Bias Hm0 [m] PRIMaRE wave buoy D
Figure 3.4: Root mean square Hm0 [m] PRIMaRE wave buoy D
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Figure 3.5: Bias Tm-1,0 [s] PRIMaRE wave buoy D
Figure 3.6: Root mean square Tm-1,0 [m] PRIMaRE wave buoy D
Figure 3.7: Number of observations PRIMaRE wave buoy D
Figures 3.8 and 3.9 give the same information as in the previous figure, but now presented in scatter
plots.
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Figure 3.8: Scatter plot Hm0 PRIMaRE wave buoy D, for different values of Tm-1,0 [s], see colour bar
Figure 3.9: Scatter plot Tm-1,0 PRIMaRE wave buoy D, for different values of Hm0 [m], see colour bar
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Error dependence on wave direction
Figure 3.10 and 3.11 show respectively the bias and scatter of Hm0 and Tm-1,0 per wave direction.
Most waves come from a westerly direction. It can be seen that most wave height errors are less
than 1 meter. The positive and negative errors cancel each other out and therefore the bias is very
small. As the wave heights are more often under- than overestimated, the bias is in most directions
slightly negative. The largest errors are found for waves from south-westerly and north-easterly
directions.
Figure 3.10: Bias and scatter Hm0 versus wave direction PRIMaRE wave buoy D
For Tm-1,0 the largest bias and root mean square errors come from waves with southerly directions.
Errors up to 4 seconds are seen. However, most errors are in the order of 1 second.
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Figure 3.11: Bias and scatter Tm-1,0 versus wave direction PRIMaRE wave buoy D
Error dependence on season
Figures 3.12 and 3.13 show the variation in time of the bias in Hm0 and Tm-1,0. For this analysis the
figures for Perranporth are shown, as Perranporth has the longest measured dataset and is also
located on the north coast of Cornwall. It can be seen that there is some monthly variation in the
errors. The larger errors are more likely to occur in the winter months than in the summer months.
Figure 3.12 also shows the mean annual variation of the bias. Each year of the dataset was divided
into spring (March, April, May), summer (June, July, August), autumn (September, October,
November) and winter (December, January, February) datasets, and the mean power calculated. It
can be seen that there is little annual variation of the bias.
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2006: -0.05 m 2007: -0.07 m 2008: -0.07 m
2009: -0.07 m 2010: -0.03 m 2011: -0.07m
2006: -2.9 s
2009: -1.6 s
2007: -1.5 s
2008: -1.5 s
2010: -1.7 s
2011: -1.7 s
Figure 3.12: Montly/annual variation of the errors in Hm0 and Tm-1,0 Perranporth
Figure 3.13: Mean monthly error for Hm0 and Tm-1,0 Perranporth
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4 Wave resources
4.1 Method
In this chapter the wave resources in the Wave Hub area are assessed. Figure 4.1 shows the area and
its bathymetry. The area is divided into four berth areas, as indicated in figure 4.1. 23-year time
series of significant wave height, wave period and direction are available for all points in this area.
Spectral output is available only at location 1, located in berth 3.
centre
Figure 4.1: Wave Hub area overview
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As spectral information is available at location 1, this point is used for a detailed assessment of the
available resources. Section 4.2 presents the 23-year time series, the joint probability of wave height
and wave period and the variability of the wave resource for time, direction and spectra.
The power, P(f), is calculated using the spectral output, S(f), and the omni-directional power
equation:
Where the group velocity is
And f is the frequency, ρ is the density of water (assumed to be 1025 kg/m3), g is gravitational
constant, k is the wave number (
and d is the water depth.
Subsequently, the spatial variation in the Wave Hub area is presented in section 4.3. To present the
variation between the different berths and inside the berths, location A-D and M are used, see figure
4.1. The power for this area is calculated in a different way than has been done for location 1, as
only the significant wave height and wave period are available. In this case an approximation is used:
The spectral period Tm-1,0 is used to calculate the wave length that is needed to calculate cg. There
are small differences in power between the two formulas. Figure 4.2 shows a scatterplot for location
1, for which the power is calculated with both equations. It can be seen that the power calculated
with the integral parameters is approximately 2% smaller than the power calculated with the
spectra. Therefore, the spatial power results, presented in section 4.3, are corrected by adding 2%
power to the calculated wave power.
1
L is the wave length and is calculated iteratively with a matlab routine
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Figure 4.2: Comparison methods of power calculation
It should be noted that the hindcast data used in this analysis hasn’t been corrected for any errors
that were found in the validation shown in chapter 3. Appendix A illustrates the effect on the shown
mean wave power, when data are corrected. The data are corrected using the regression formulas
for PRIMaRE wave buoy D, see figure 1 and 2 in appendix A. As the spatial correlation between
PRIMaRE wave buoy D and Wave Hub is high (shown in appendix A), it is assumed that the necessary
error correction for Wave Hub is the same as for PRIMaRE wave buoy D. However, there could be
some difference in the errors, as the waves are usually higher at PRIMaRE wave buoy D than at
Wave Hub. The difference between the uncorrected and corrected wave power is large,
approximately 7 kW/m for the mean wave power at location 1. This is due to the relatively large
error in the wave period.
4.2 Data analysis location 1
In this section the wave resources are presented by means of:
• time series of wave power, Hm0 and Tm-1,0
• Joint probability plot between Hm0 and Tm-1,0
• Power variation in time
• Directional variation of wave power
• Spectral variation
Time series
In figure 4.3 the 23-year time series for wave power, Hm0 and Tm-1,0 at location 1 are shown. The
mean value for each parameter is given in the figure. At location 1 the mean power is 20 kW/m. This
agrees with values found in the wave resource assessment that was conducted with the available
measurement data, see ‘Assessment of the Wave and Current Resource at the Wave Hub Site’,
January 2011.
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Figure 4.3: Timeseries power, Hm0 and Tm-1,0 at location 1, not corrected for hindcast error
Joint probability
Figure 4.4 shows the joint probability for Hm0 and Tm-1,0 at location 1. Every square shows the
occurrence of the combination of Hm0 and Tm-1,0 in percent. It can be seen that the most occurring
waves have a wave height of approximately 1-2 meters and a wave period of 4-7 seconds.
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Figure 4.4: Joint probability Hm0 and Tm-1,0 at location 1, not corrected for hindcast error
Variation in time
Figure 4.5, 4.6 and 4.7 show the annual and monthly variation in wave power, Hm0 and Tm-1,0 at
location 1. In addition figure 4.8 presents the seasonal power variation, for which each year of the
dataset was divided into spring (March, April, May), summer (June, July, August), autumn
(September, October, November) and winter (December, January, February) datasets, and the mean
power was calculated. The variation in power levels over each year is substantial, with average
monthly power levels over 50 kW/m in some winter months, compared with frequent monthly
averages below 10 kW/m in the summer months. The figure in the mid panel suggests an overall
trend of decreasing power levels. The values agree with the values found for MetOffice location
‘U04’ in the wave resource assessment that was conducted with the available measurement data,
see ‘Assessment of the Wave and Current Resource at the Wave Hub Site’, January 2011. This is
shown in appendix B Averaged over the whole dataset, it can be seen that December, January and
February are the most energetic months with mean power levels up to 40 kW/m.
Wave heights vary from 1.3 meter in summer to 2.8 meter in winter. Wave periods vary from 6
seconds in summer to 9 seconds in winter.
Finally, figure 4.9 shows the annual cumulative probability distribution of the wave power. The curve
for the average distribution in the upper pannel of figure 4.9 shows that 95% of sea states have a
power of 100kW/m or less. Furthermore it can be seen in the lower pannel of figure 4.9 that the
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proportion of sea states with a power of less than 15kW/m varies from approximately 56% for the
most energetic year to 76% for the least.
Figure 4.5: Montly/annual variation of power at location 1, not corrected for hindcast error
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Figure 4.6: Montly/annual variation of Hm0 at location 1, the bars are showing the standard deviation in the data, not
corrected for hindcast error
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Figure 4.7: Montly/annual variation of Tm-1,0 at location 1, the bars are showing the standard deviation in the data
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Figure 4.8: Seasonal variation of power at location 1, not corrected for hindcast error
Figure 4.9: Annual wave power cumulative probability distribution for location 1, upper panel: power up to 500 kW/m,
lower panel: power up to 50kW/m, including the mean distribution (not corrected for hindcast error)
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Directional variation
Figure 4.10 shows the directional wave power variation. The left-hand figure shows the occurrence
of wave power smaller than 50 kW/m and the right-hand figure shows the occurrence of wave
power larger than 50 kW/m. It can be seen that most wave energy comes from the west and in
addition the most energetic waves come from the west.
Figure 4.10: Wave rose for wave power [kW/m] at location 1, left-hand figure for power < 50 kW/m, right-hand figure for
power > 50 kW/m (not corrected for hindcast error)
Figure 4.11 shows the mean wave power binned by wave direction. The mean wave power is largest
for wave directions between 240 and 300° North, with respectively 26 kW/m and 24 kW/m for the
240-270 and 270-300° bins. The joint probability between Hm0 and Tm-1,0 is shown for these bins in
figure 4.12 and 4.13. Figures 4.12 and 4.13 show that the most occurring waves for the westerly
wave directions are larger than when the joint probability for all directions is shown, as in 4.4. The
joint probability diagrams for the remaining directions are shown in appendix C.
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Figure 4.11: Mean wave power [kW/m] binned by wave direction [°N] in 30 degree bins (not corrected for hindcast error)
Figure 4.12: Joint probability Hm0 and Tm-1,0 for wave direction bin 240-270° (not corrected for hindcast error)
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Figure 4.13: Joint probability Hm0 and Tm-1,0 for wave direction bin 270-300° (not corrected for hindcast error)
Spectral variation
Figure 4.14 presents spectral data in a scatter diagram format. For each bin of the scatter diagram, all
spectra with parameters that fall within the bin limits are plotted and the mean spectrum for the bin is
calculated. The figure indicates that bi-model sea states occur.
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2
Figure 4.14: spectral variation, with frequency [Hz] on the x-axis and energy density [m /Hz] on the y-axis (not corrected for
hindcast error)
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4.3 Spatial variation in Wave Hub area
The spatial variation in mean wave power is shown in figure 4.15. Note that the wave power is
calculated with integral parameters instead of spectra and subsequently corrected, see section 4.1.
A difference of circa 3 kW/m is present in the area.
Figure 3.16 shows the mean wave power relative to location 1. The results of section 4.2 can be
translated to other locations in the Wave Hub area with the help of this figure.
Finally, figure 3.17 gives a comparison of mean wave power between the berths and inside the
berths. The mean power for each berth is shown in the figure. It can be seen that berth 4 is the most
energetic, while berth 1 is the least energetic. However, mean wave power also varies inside the
berths, with differences up to 0.5 kW/m.
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centre
Figure 4.15: spatial variation mean wave power for Wave Hub area with bathymetry contours (not corrected for hindcast
error)
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centre
Figure 4.16: spatial variation mean annual wave power relative to power at location 1 for Wave Hub area with bathymetry
contours (not corrected for hindcast error)
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Figure 4.17: Power variation between berths and inside berths and mean wave power per berth (not corrected for hindcast
error)
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5 Conclusions
Hindcast validation
• The agreement between computed and measured significant wave height is very good, in
particular for operational wave conditions.
• However, extreme wave heights are often underestimated by the wave model. This means that
the analysis of extreme waves becomes more uncertain. By means of bias correction (see
appendix A) and random error correction (not done for this study) the hindcast errors can be
taken into account.
• In addition, the wave period is often underestimated by the wave model. This has large
consequences for the calculation of wave power. By means of bias correction the bias can be
taken into account (see appendix A).
Wave resources
• The average wave power at Wave Hub is approximately 20 kW/m. When the bias on the
hindcast results is corrected the average wave power is 7 kW/m higher.
• The wave power varies with time, wave direction and space:
o As can be expected, the wave power is highest in the winter months with mean
yields of 40 kW/m and lowest in summer with mean yields of 10 kW/m.
o Westerly waves have the largest wave power, with a mean of approximately 25
kW/m.
o The mean wave power at Wave Hub varies with approximately 3 kW/m, depending
on location. The variation is mainly due to bathymetry variation.
Discussion
The quality of the hindcast conducted for this study is largely depending on the resolution and
quality of the wave boundary and wind input. In this study the freely available ECMWF2 global
hindcast was used. As was shown in figure 2.2, the spatial and time resolutions of the ECMWF
hindcast are very coarse. As a result extreme wind and wave occurrences are averaged out in time
and space and this can explain why the SWAN hindcast conducted for this study tends to
underestimate extreme waves.
Ocean wave reanalysis data for the British Isles at a higher resolution (than the ECMWF hindcast) is
available and can be purchased at various weather institutes, for example the Met Office. In case
higher accuracy hindcast data is required, it is recommended to rerun the hindcast with the higher
resolution input data.
In addition, the wave boundary conditions for the SWAN hindcast were based on the wave
parameters Hm0, Tm01 and wave direction for which a JONSWAP spectral shape was assumed.
Spectral boundary input or partitioned wave boundary input can improve the quality of the hindcast
as the occurrence of multi modal sea states on the wave boundary can be taken into account.
2
European Centre for Medium-Range Weather Forecasting
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Ocean wave reanalysis data for the British Isles with partitioned wave parameters is available and
can be purchased at various weather institutes, for example the Met Office. In case higher accuracy
hindcast data is required, it is recommended to rerun the hindcast with partitioned wave input.
Finally, appendix A presents a correction on the hindcast data. The presentation of the corrected
data is meant to show the effect of the hindcast errors on wave power. However, the correction was
based on a simple regression technique. A more extensive study of the correction terms would be
advisable, before the corrected hindcast values can be used.
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Literature
Bathymetry, Marine Digimap
Booij, R.C. Ris, N., Holthuijsen, L.H. (1999). A third-generation wave model for coastal regions, Part I,
7649-7666.
Model description and validation. Brooker, D.C., Cole, G.K., McConochie J.D. (2004). The influence of hindcast modeling uncertainty on
OMAE2004-51161
the prediction of high return period wave conditions. Nieuwkoop-McCall, J.C.C. van (2011). A wave model for the Cornwall coast: Phase 1: Wave model
set-up and sensitivity study. University of Exeter. Rogers, W.E., Hwang, P. A., & Wang, D. W. (2003). Investigation of Wave Growth and Decay in the
SWAN Model: Three Regional-Scale Applications. , !!(2), 366-389.
Smith, H.M., Haverson, D., Smith, G.H., Cornish, C.S., Baldock, D. (2011). Assessment of the Wave
and Current Resource at the Wave Hub Site. University of Exter. .
WAFO group (2011). WAFO – a Matlab toolbox for analysis of random waves and loads. Lund
$ % & '
University. " #
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Hindcast Wave Hub
Appendix A Analysis corrected hindcast data
Regression of the hindcast error
Separate corrections for Hm0 and Tm-1,0 are determined using regression techniques. Figures 1 and 2
show the error in Hm0 or Tm-1,0 relative to the computed value of Hm0 or Tm-1,0 for PRIMaRE buoy D. In
addition the bin-averaged bias is shown and a regression line is drawn. The bias in Hm0 is modelled as
quadratic, the bias in Tm-1,0 is modelled as constant.
The trend lines of the errors in the computed values of Hm0 and Tm-1,0 can be used to correct the
hindcast values at the PRIMaRE wave buoy location. Whether the correction is also valid at the Wave
Hub location, depends on the spatial correlation between the locations. Figure 3 shows that the
correlation between these locations is high.
x2
x +
Figure 1: Regression BIAS Hm0 PRIMaRE wave buoy D
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Figure 2: Regression BIAS Tm-1,0 PRIMaRE wave buoy D
Figure 3: Spatial correlation between Wave Hub location 1 (ADCP) and PRIMaRE wave buoy D for Hm0 and Tm-1,0
Wave resources
Figures 4 and 5 show the comparison between the corrected and uncorrected hindcast datasets.
Figure 5 also shows the mean power, Hm0 and Tm-1,0 for the corrected dataset and the uncorrected
dataset (in brackets). Furthermore, figure 6 shows the joint probability for Hm0 and Tm-1,0 at location
1. Every square shows the occurrence of the combination of Hm0 and Tm-1,0 in percent.
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Figure 4: Comparison Corrected (red) and uncorrected (blue) timeseries power, Hm0 and Tm-1,0 at location 1.
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Figure 5: Comparison monthly/annual variation of power at location 1 for corrected and uncorrected hindcast datasets
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Figure 6: Joint probability Hm0 and Tm-1,0 at location 1, corrected for hindcast error
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Appendix B Relation to previous studies
Figure 2 compares the hindcast values with values calculated in the wave resource assessment that
was conducted with the available measurement/model data, see ‘Assessment of the Wave and
Current Resource at the Wave Hub Site’, January 2011. Both the corrected and the uncorrected
hindcast results are shown in the figure. The locations of the aforementioned report are shown in
figure 1. The ‘PWB’ are the PRIMaRE wave buoys, Met Office (indicated as MO_WW3 in figure 6) is
the most recent Met Office wave model utilising WaveWatchIII, U04 is a grid point from the previous
Met Office wave model and SWM is the Sea Watch Mini buoy.
Figure 1: Measurement/ model locations ‘Assessment of the Wave and Current Resource at the Wave Hub Site’, January
2011
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Figure 2: Comparison annual mean wave power with ‘Assessment of the Wave and Current Resource at the Wave Hub
Site’, January 2011
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Appendix C Directional variation
Figures 1 to 12 show the joint probability diagrams for 30 degree directional bins.
Figure 1: Joint probability Hm0 and Tm-1,0 at location 1 for 0-30°, for the uncorrected hindcast data
Figure 2: Joint probability Hm0 and Tm-1,0 at location 1 for 30-60°, for the uncorrected hindcast data
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Figure 3: Joint probability Hm0 and Tm-1,0 at location 1 for 60-90°, for the uncorrected hindcast data
Figure 4: Joint probability Hm0 and Tm-1,0 at location 1 for 90-120°, for the uncorrected hindcast data
Figure 5: Joint probability Hm0 and Tm-1,0 at location 1 for 120-150°, for the uncorrected hindcast data
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Figure 6: Joint probability Hm0 and Tm-1,0 at location 1 for 150-180°, for the uncorrected hindcast data
Figure 7: Joint probability Hm0 and Tm-1,0 at location 1 for 180-210°, for the uncorrected hindcast data
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Figure 8: Joint probability Hm0 and Tm-1,0 at location 1 for 210-240°, for the uncorrected hindcast data
Figure 9: Joint probability Hm0 and Tm-1,0 at location 1 for 240-270°, for the uncorrected hindcast data
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Figure 10: Joint probability Hm0 and Tm-1,0 at location 1 for 270-300°, for the uncorrected hindcast data
Figure 11: Joint probability Hm0 and Tm-1,0 at location 1 for 300-330°, for the uncorrected hindcast data
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Figure 12: Joint probability Hm0 and Tm-1,0 at location 1 for 330-360°, for the uncorrected hindcast data
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