ANGEOAnnales GeophysicaeANGEOAnn. Geophys.1432-0576Copernicus PublicationsGöttingen, Germany10.5194/angeo-34-1197-2016Spatial and temporal variations of wave energy in the nearshore waters of
the central west coast of IndiaAmruthaM. M.Sanil KumarV.sanil@nio.orgOcean Engineering Division, Council of Scientific and Industrial
Research – National Institute of Oceanography (CSIR-NIO), Dona
Paula, Goa, 403 004, IndiaV. Sanil Kumar (sanil@nio.org)16December201634121197120824September201618November201628November2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://angeo.copernicus.org/articles/34/1197/2016/angeo-34-1197-2016.htmlThe full text article is available as a PDF file from https://angeo.copernicus.org/articles/34/1197/2016/angeo-34-1197-2016.pdf
Assessment of wave power potential at different water depths and
time is required for identifying a wave power plant location. This study
examines the variation in wave power off the central west coast of India at
water depths of 30, 9 and 5 m based on waverider buoy measured wave data.
The study shows a significant reduction (∼ 10 to 27 %) in wave
power at 9 m water depth compared to 30 m and the wave power available at
5 m water depth is 20 to 23 % less than that at 9 m. At 9 m depth, the
seasonal mean value of the wave power varied from 1.6 kW m-1 in the
post-monsoon period (ONDJ) to 15.2 kW m-1 in the Indian summer monsoon
(JJAS) period. During the Indian summer monsoon period, the variation of wave
power in a day is up to 32 kW m-1. At 9 m water depth, the mean
annual wave power is 6 kW m-1 and interannual variations up to
19.3 % are observed during 2009–2014. High wave energy
(> 20 kW m-1) at the study area is essentially from the directional
sector 245–270∘ and also 75 % of the total annual wave energy is
from this narrow directional sector, which is advantageous while aligning the
wave energy converter.
History of geophysics (ocean sciences) – meteorology and atmospheric dynamics (waves and tides)Introduction
The generation of electricity and heat is responsible for 41 % of the
annual global carbon dioxide emissions from fuel combustion in 2011 (IEA,
2013). Replacing the present energy sources with renewable energy sources can
reduce the global carbon dioxide emissions significantly. Ocean waves have
the potential to become a commercially viable renewable energy source
(Clement et al., 2002). Globally, wave energy resource assessments have been
made for the Baltic Sea, the Black Sea, the Hawaiian islands, the North Sea,
the Persian Gulf and for the seas around Australia, Brazil, Canada,
California, Canary Islands, China, India, Iran, Ireland, Malaysia, Portugal,
Taiwan, the United Kingdom and the United States (Barstow et al., 2008; Defne
et al., 2009; Stopa et al., 2011; Saket and Etemad-Shahidi, 2012; Kamranzad
et al., 2013; Gonçalves et al., 2014; Soares et al., 2014; Appendini et
al., 2015; Contestabile et al., 2015; Rusu, 2015; Sanil Kumar and Anoop,
2015; Gallagher et al., 2016). Most of the studies on the assessment of wave
power are carried out either through the wave data obtained from numerical
model or reanalysis data; ERA-40 or ERA-Interim (Dee et al., 2011) of the
European Centre for Medium-Range Weather Forecasts (ECMWF). The
intercomparisons of measured energy period with ERA-Interim mean wave period
suggest that the data of the latter show an encouraging agreement with the
energy period (Contestabile et al., 2015). Sanil Kumar and Anoop (2015)
compared the significant wave height based on ERA-Interim and that estimated
from a waverider buoy from June to August in the northern Arabian Sea and
reported that the mean error is within 5 %. A 10 % error in the
estimate of surface wind speed can lead to a 10–20 % error in significant
wave height (Hs) and a 20–50 % error in wave energy (Cavaleri,
1994). Hence, it is important to know how the estimate of wave energy based
on the reanalysis data differ from that obtained from measured data over an
annual cycle.
India has a long coastline of 5423 km along the mainland, annually
receives around 5.7 million waves and has large wave energy resources (Sanil
Kumar and Anoop, 2015). Along the coastal waters of India, the Indian
Institute of Technology Madras in Chennai has conducted early studies on wave
energy resources and wave energy conversion devices (Ravindran and Koola,
1991). In addition, a wave energy plant is located on the southwest coast of
India at Vizhinjam, based on the nearshore oscillating water column (Ravindran
and Koola, 1991; Mala et al., 2011). Based on the measured wave data covering
a 1-year period, Sanil Kumar et al. (2013) reported temporal variations in
nearshore wave power at four shallow water locations covering the east and
west coasts of India. Recently, Sanil Kumar and Anoop (2015) examined the
long-term variations in wave power at 19 deep water locations covering the
Indian shelf seas based on ERA-Interim data.
Precise estimates of wave energy resources at close spatial and temporal
resolution are required for planning and design of wave energy converters.
The waves in the Arabian Sea show strong seasonal variation (Sanil Kumar and
Anoop, 2015) with high waves during the Indian summer monsoon (June to
September, hereafter referred as monsoon). The variability of the wave power
in different time scales (monthly, seasonal and annual) needs to be known
before finalizing a location for a wave power plant, since locations with
steady wave power are preferred than locations with large seasonal and annual
variations (Sanil Kumar and Anoop, 2015). Nowadays, most of the wave energy
assessments are made in deep water to take advantage of the resource (which
is larger) and most of the wave energy converters (WECs) are generally
designed to be deployed at water depths greater than 25 m (e.g., the Wave
Dragon; Kofoed et al., 2006) or even 50 m (e.g., the Pelamis; Henderson,
2006). A great challenge for wave power is the logistics of building a wave
farm and connecting the cable to the mainland (Rusu, 2014). The capital
investment is less if the wave power plant is closer to the coast. Hence, the
deployment of WECs at shallower waters presents undoubtable advantages as
lower mooring costs or cheaper and easier connection to the electrical
network, which can compensate for a lower resource (as a consequence of
energy dissipation due to bottom friction). In addition, some types of WECs
(like oscillating water column; Falcao and Henriques, 2016) can operate in
relatively shallow waters. Also in shallower water depths, the motion of
water particles under a wave will be in horizontal ellipse, i.e., the
horizontal back-and-forth surging motion is larger than the vertical
up-and-down motion and at such locations different types of wave generation
system can be planned than that used in deep water, where oscillatory motion
is circular and diminishes exponentially with depth (URS, 2009), Therefore,
the spatial variation of the wave resource along the nearshore area is a
topic worthy of being investigated. No previous studies on the variation in
wave power at different water depths across the shore based on measured wave
data have been carried out in Indian waters. It is also essential to understand how the wave energy is
distributed with respect to wave period and direction. Hence, the purpose of
this research is to assess the change in wave energy from 30 to 9 m and from
9 to 5 m water depth and its temporal variations. The interannual variations
in wave power at 9 m water depth from 2009 to 2015 are also examined. The
wave power estimated from ERA-Interim data is compared with that computed
based on the measured wave data. The directional distribution of wave power
is also required when selecting a wave power plant orientation and hence this
aspect is also studied. The paper is organized as follows: Sect. 2 contains
the data and methodology used in the study, Sect. 3 describes the results,
Sect. 4 contains a discussion of the results and Sect. 5 summarizes the
conclusions.
Map showing the study area. The black dots indicate the waverider
buoy locations at 30, 9 and 5 m water depths. The open circle indicate the
ERA-I grid point.
Location and time period of data used in the study in different
years.
LocationPeriodNumberHs (m) Tz (s) Te (s) Waveof datapower(kW m-1)RangeMeanRangeMeanRangeMeanMean9 m water depth1 Jan–31 Dec 200915 9210.21–4.371.032.5–11.15.64.1–14.68.55.8(14.304∘ N,(90.9 %)74.391∘ E)1 Jan–31 Dec 201017 4590.22–3.701.012.5–9.85.54.1–15.08.35.8(99.7 %)1 Jan–31 Dec 201117 4210.26–3.821.042.9–11.45.74.1–15.88.66.3(99.4 %)1 Jan–31 Dec 201217 5240.29–3.411.043.0–8.95.54.4–14.18.45.7(99.7 %)1 Jan–31 May and11 5960.26–1.800.702.8–10.85.14.3–16.08.22.01 Oct–31 Dec 2013(66.2 %)1 Jan–31 Dec 201417 4290.23–4.091.082.6–9.55.74.3–14.98.87.2(99.5 %)1 Jan–31 Dec 201517 2580.27–4.340.992.8–11.15.64.2–16.28.85.4(98.5 %)30 m water depth18 Apr–18 Aug 201458290.47–4.381.942.9–9.36.05.1–13.28.622.4(14.307∘ N,(99.7 %)74.291∘ E)1 Jun–31 Jul 201529280.71–5.022.263.9–8.36.46.2–10.88.423.2(100 %)5 m water depth22 Apr–17 Dec 201197510.26–3.671.273.2–10.36.45.4–16.59.37.3(14.304∘ N,(84.6 %)74.414∘ E)1 Jun–31 Jul 201528010.56–4.951.764.0–9.86.56.1–15.88.912.0(96 %)Materials and methodsWave data
Measured wave data obtained from moored Datawell directional waverider buoys
off Honavar (Fig. 1) are used in the study. The details of the measurements
carried out at 5 m water depth (14.304∘ N, 74.414∘ E),
9 m (14.304∘ N, 74.391∘ E) and 30 m water depth
(14.307∘ N, 74.291∘ E), and the length of data used in the
study at each location are presented in Table 1. The distance of the 5, 9 and
30 m waverider buoy from the coast are 0.4, 2.4 and 16.4 km, respectively, indicating that the
measurement locations are within the territorial waters of the country. At
9 m water depth, the wave data were collected from 1 January 2009 to
31 December 2015. Due to interferences with local fishing boats, the buoy
drifted from the moored location and hence continuous data could not be
collected at 9 m water depth during July 2013. Also, in all years, the buoy
and the moorings are retrieved and redeployed after removing the biofouling
from the buoy hull and the mussel growth from the mooring line. Hence, the
data available for analysis in different years varies from 90 to 99.7 %
except in 2013 (Table 1). At 30 and 5 m water depth data were collected for
a limited period (Table 1), which covers pre-monsoon (low wave condition) and
monsoon (high wave activity). The interannual variations in wave spectral
characteristics of the study area are presented by Sanil Kumar and
Anjali (2015). For studying the trends in climate, the rule of thumb is to
use ∼ 30 years of data. Since the measured data are for a short period
of 6 years, the significant wave height and mean wave period from the
ERA-Interim (ERA-I) reanalysis data set (Dee et al., 2011) produced by the
ECMWF for points (14.250∘ N, 74.250∘ E) close to the buoy
location at 30 m water depth for 37 years (1979 to 2015) is used to study
the seasonal and interannual changes in mean wave power.
The wave spectrum is obtained from the heave data recorded by the buoy
through fast Fourier transform (FFT). The significant wave height
(Hs) and the energy period (Te) are obtained from the
spectral moments using Eqs. (1) and (2).
Hs=4m0
Te=m-1m0
Where mn is the nth-order spectral moment and given by mn=∫0∞fnS(f)df, n=0 and -1, and S(f) is the
spectral energy density at frequency f.
Wave power estimation
Wave parameters are converted to the wave power transmitted per unit width
by using the expression given below (Mørk et al., 2010).
P=ρg∫02π∫0∞Cgf,dS(f,θ)dfdθ
Where P is the wave power per unit of crest length (kW m-1), ρ
is the density of seawater (kg m-3), g is the gravitational
acceleration (m s-2), Cg is the group velocity (m s-1),
S(f,θ) is the directional wave spectrum (m2 Hz-1), d is
the water depth (m) and θ is the wave direction (∘). The
seawater density varies temporally based on the salinity and temperature and
for the present study, an average value of 1025 kg m-3 is adopted.
Scatter plot of wave power at 9 and 30 m water depth (a, c). Wave power at 5 and 9 m water depth (b, d) in different
years.
When the data on wave spectrum is not available, and only the bulk wave
parameters Hs and Te are available, wave power is
estimated based on Eq. (4), derived for the deep water location. We have
compared the wave power estimation based on Eq. (4) with that obtained from
Eq. (3) to better understand the validity of Eq. (4) in shallow waters.
P=ρg264πHs2Te
From each half-hour wave data pair (Hs, Te), the related
wave power is computed in kW m-1. The average of the power is computed
in order to get the monthly and yearly mean wave power. In some of the
earlier studies (Kamranzad et al., 2013; Sierra et al., 2013), since energy
period (Te) values are not readily available, the same is estimated
from the peak wave period (Tp) using the expression Te=0.9Tp (Contestabile et al., 2015). The validity of this equation
for the study area is also examined.
Scatter plot of wave parameters at 9 and 30 m water
depth (a) significant wave height, (b) mean wave period and
(c) mean wave direction. Scatter plot of wave parameters at 5 m and
9 m water depth (d) significant wave height, (e) mean wave
period and (f) mean wave direction.
Variation of wave power with significant wave height at 9 m water
depth based on measured data during 1 January 2009 to 31 December 2015. The
color bar indicates the occurrence probability of the measured data.
Statistically the comparison between two data sets (Ai and Bi) are
carried out using Pearson's linear correlation coefficient (r), bias and
root-mean-square error (RMSE).
r=∑i=1N(Ai-A‾)(Bi-B‾)∑i=1N(Ai-A‾)2(Bi-B‾)2bias=1N∑i=1N(Ai-Bi)RMSE=1N∑i=1N(Ai-Bi)2
Where N is the number of data points and the overbar represents the mean
value.
ResultsSpatial variation of wave power
The wave data measured simultaneously at 30 and 9 m water depth during 2014
and at 9 and 5 m water depth during 2011 and at all the three water depths
during June to July 2015 are used to study the spatial variations in wave
power. The horizontal distance between the locations at 30 and 9 m water
depth is 14 km and the distance between the locations at 9 and 5 m water
depth is 2 km. As the waves approach the coast, the waves lose energy mainly
by wave breaking and by friction against the seabed. The average wave power
during 18 April–18 August 2014 at 30 and 9 m water depth are 22.4 and
16.5 kW m-1, respectively, whereas the maximum wave power values at
these depths are 122.7 and 78 kW m-1. The wave power available at 9 m
water depth is 10 to 27 % less than that at 30 m (Fig. 2a). The RMSE
between the wave power at 30 and 9 m water depth is 9.8 kW m-1 and
the bias is 5.9 kW m-1. Conversely, the Hs at 9 m water
depth is approximately 15 % less than the value at 30 m (Fig. 3a) with
the mean value of 1.9 and 1.8 m at 30 and 9 m water depth, respectively.
Whereas, no significant reduction is observed in mean wave period
(Tm02) at 9 m water depth (∼ 6.3 s) compared that at
30 m water depth (∼ 6 s) (Fig. 3b). Similarly, during 1 June to
31 July 2015, the reduction in mean wave power from 30 to 9 m water depth is
around 20–26 % (Table 1 and Fig. 2c).
The average wave power during 22 April–17 December 2011 at 9 and 5 m water
depth are 9.2 and 7.3 kW m-1, respectively. At 5 m water depth, the wave power available is 20 %
less than that at 9 m (Fig. 2b). The RMSE between the wave power at 9 and
5 m water depth is 3.5 kW m-1 and the bias is 1.9 kW m-1.
Compared to the observation between the 30 and 9 m water depth, the
Hs at 5 m water depth is only 5 % less than the value at 9 m
water depth (Fig. 3d) with a mean value of 1.3 m at both the 9 and 5 m
water depth. The reduction in mean wave power from 9 to 5 m water depth
during 1 June to 31 July 2015 is around 23 % and from 30 to 5 m water
depth is ∼ 48 % (Table 1 and Fig. 2d).
Even though the wave power varies with wave height and group velocity/energy
period, the variation is strongly related to Hs than other
parameters since the wave power depends on the square of Hs. A
study by Sanil Kumar et al. (2013) showed that the wave power in the
nearshore waters can be estimated approximately based on the expression P=4.5×Hs2, in spite of the fact that waves in the nearshore
waters will be in intermediate waters for most of the sea states. The present
study also shows that if only Hs is known, wave power can be
estimated using this approximate expression with a correlation coefficient of
0.99, bias of -0.85 kW m-1 and RMSE of 1.33 kW m-1 (Fig. 4).
The mean wave power based on approximate expression is (6.90 kW m-1) higher than that
(6.05 kW m-1) estimated based on wave spectrum. The wave power
estimated based on the ERA-I significant wave height and wave period data is
lower than the value estimated from the measured data at 30 m water depth
for high values (> 20 kW m-1) and the bias is 3 kW m-1 with
a RMSE of 8 kW m-1 (Fig. 5). The ERA-I Hs for the same
period is also lower than the measured Hs for values more than
2 m. The mean wave period from ERA-I also shows scatter (r=0.7) compared
to the measured Te data. Hence, the wave power estimate based on
ERA-I can be used only as a preliminary estimate in locations in the eastern
Arabian Sea where there is no measured wave data.
Scatter plot of (a) significant wave height
(b) energy period and (c) wave power based on the measured
data at 30 m water depth and that estimated from ERA-I during 19 April
to 18 August 2014.
The wave energy period is a sea state parameter that is not readily available
like Tm02 and Tp. Hence, some researchers (e.g.,
Kamranzad et al., 2013; Contestabile et al., 2015) estimated the energy
period from the peak wave period using the expression Te=0.9Tp. The comparison of wave power estimated based on
0.9 Tp with that based on Te using Eq. (4) shows larger
scatter (Fig. 6). Sanil Kumar and Anoop (2015) observed that for locations in
the Arabian Sea and the Bay of Bengal where long period swells
(Tp> 12 s) are present, estimating wave power using
0.9 Tp as the energy period will lead to overestimation of wave
power for values of Tp more than 10 s and underestimation of
Te for values of Tp less than 10 s. In the present study
area at 9 m water depth, during 52 % of the time, Tp is more
than 12 s with an average value of 14.3 s and during the same period, the
average value of Te is only 8.8 s. Hence, large overestimation can
happen if the wave power is estimated based on Tp. Sanil Kumar et
al. (2013) also found that the expression Te=0.9Tp is
not valid at four shallow water locations around India (water depth 9 to
15 m) when Tp is more than 8 s.
Scatter plot of wave power based on the measured data at 9 m water
depth and that estimated from Eq. (4) with Te and
Te=0.9Tp during January to December in different
years.
Scatter plot of significant wave height with energy period at 9 m
water depth during January 2009 to December 2015. The color bar indicates the
occurrence probability of the measured data.
Range and percentage variation of wave power in a given day in
different years.
For the wave data considered in the study at 9 m water depth, intermediate
and shallow water conditions exist for almost all of the time. Hence, the
wave power estimated based on the deep water Eq. (4) is ∼ 10 % more
than that estimated based on Eq. (3) using the measured data (Fig. 6). Here,
Hs and Te were obtained from the wave spectrum of the
buoy measured data. The study shows that the wave power estimate based on
approximate Eq. (4) using only the Hs and Te will lead to
overestimation of wave power in shallow waters.
It is observed that the distribution of Hs with respect to
Te follows mainly two patterns: (i) a narrow distribution of
Te (7–11 s) for a wide range of Hs values (0.5–4.5 m)
and (ii) a broad distribution of Te (4–16 s) for a narrow range
of Hs (Fig. 7). The narrow distribution of Te is during
the monsoon period and the broad distribution of Te is during the
non-monsoon period when the Hs is less than 1.5 m.
Daily variation in wave power varied from 0.1 to 37 kW m-1 with an
average value of 3.7 kW m-1 (Fig. 8). Sanil Kumar et al. (2013)
observed a daily variation in wave power from 0.2 to 40 kW m-1 and the
average daily wave power from 0.4 to 56 kW m-1 for coastal locations
around India. This large variation in daily wave power is due to the
influence of monsoon, which creates a large difference in daily wave height
(daily average Hs varying from 0.1 to 1.8 m) and wave period.
Earlier studies off the west coast of India show diurnal variation in bulk
wave parameters due to the sea breeze mainly during the pre-monsoon (Sanil
Kumar and Anjali, 2015). The change in wave power due to the sea breeze is
studied through the plot of hourly averaged wave power with time in different
months (Fig. 9). Figure 9 indicates that during January to May and December,
due to the sea breeze, the wave power is highest during 16:00–18:00 UTC.
Hourly variation of mean wave power in different months.
Monthly variations in wave power at 9 m water depth
The monthly average wave power variation in different years at 9 m water
depth is presented in Fig. 10. Monthly average wave power varies from
1 kW m-1 in December to 19.7 kW m-1 in July. In all years, the
monthly mean wave power is highest during the months of
June or July. During 2009–2015, the highest monthly mean wave power
(∼ 26.9 kW m-1) occurred in July 2014. The mean wave power
during June–August is more than 25 kW m-1 at deepwater locations
(Sanil Kumar and Anoop, 2015). For the study location during the non-monsoon
period, the average monthly wave power is less than 5 kW m-1 in all
years. To determine the monthly variability in wave power, the monthly
variability index (MVI) is used (Cornett, 2008). The MVI is the ratio of the
difference between the maximum and minimum monthly average wave power and the
annual average wave power. The present study indicates that the wave power
variability is greater in all years with MVI values ranging from 3 to
3.8. Small values of the MVI indicate less variability in wave
power.
Monthly average wave power in different years at 9 m water depth
Range and average value of the wave power at 9 m water depth during
different seasons of different years.
YearWave power (kW m-1) Pre-monsoon (FMAM) Monsoon (JJAS) Post-monsoon (ONDJ) Full year RangeAverageRangeAverageRangeAverageRangeAverage20090.40–19.622.981.20–97.4012.870.16–31.702.040.14–84.815.7820100.30–12.862.190.92–68.9315.570.19– 8.031.420.17–59.945.8320110.29–7.362.001.59–69.2116.940.28–10.821.600.24–61.206.2620120.41–9.262.221.04–49.2414.880.34–7.761.580.29–44.695.7420130.33–10.282.36––0.27–10.611.62––20140.38–8.292.021.19–77.9518.210.2–8.161.330.2–77.957.2320150.29–7.141.971.35–107.7812.590.29–11.121.600.29–108.785.44Seasonal variations in wave power at 9 m water depth
The waves in the Indian shelf seas show seasonal variations (Glejin et al.,
2013; Sajiv et al., 2012) with high waves (Hs> 1.5 m) during
the monsoon. February to May is the pre-monsoon period, while October to
January is the post-monsoon period. Hence, the seasonal variations in wave
power are examined and the findings show that the highest seasonal mean wave
power occurs during the monsoon (Table 2). The average wave power during the
monsoon varied from 12.6 kW m-1 (in 2015) to 18.2 kW m-1 (in
2014) (Table 2). The study based on ERA-I data at 30 m water depth shows
that the average wave power during the monsoon period varied from
15.54 kW m-1 (in 1987) to 26.08 kW m-1 (in 1994) with an
average value of 20.75 kW m-1. At 9 m water depth, the seasonal
average wave power varied from 1.97 to 2.98 kW m-1 during the
pre-monsoon and 1.33 to 2.04 kW m-1 during the post-monsoon (Table 2).
Interannual variations in wave power at 9 m water depth
Interannual variations in wave climate are reported in many studies (Gulev
and Grigorieva, 2004; Shanas and Sanil Kumar, 2014). When further
investigating the correlation between the available wave power in different
years, it was found that the annual mean wave power was identical
(∼ 5.8 kW m-1) in 3 out of 6 years studied at 9 m water depth.
Compared to the other years, the annual mean Hs and Te
are maximum (1.08 m and 8.8 s) in 2014 and hence the annual mean wave power
is also high (∼ 7.2 kW m-1) in 2014. The percentage distribution
of wave power available in different ranges during an annual cycle in
different years are presented in Table 3. The table shows that, in all years,
wave power more than 10 kW m-1 is available during 16 % (2015) to
22 % (2012) in a year. The study shows that the interannual variations in
annual mean wave power (∼ 6 kW m-1) during 2009 to 2015 at 9 m
water depth based on measured data are 3.8 to 19.3 % (Table 2). The
interannual variations in wave power are due to the interannual variations in
the wave spectrum observed in all months with larger variations during
January–February, May and October–November as a result of the variations in
the wind-sea and the swells propagating from the southern Indian Ocean
(Glejin et al., 2013; Sanil Kumar and Anjali, 2015). The study based on ERA-I
data at 30 m water depth shows that the average annual wave power varied
from 7.18 kW m-1 (in 1987) to 10.69 kW m-1 (in 1994) with an
average value of 8.98 kW m-1 (Fig. 11).
Directional distribution of wave power at 9 m water depth
The directional distribution of wave power is required when selecting the
orientation of a wave power plant. At 9 m water depth, the high wave energy
(> 20 kW m-1) is essentially from the 245–270∘ sector and
less energetic waves are in the direction between 225 and 245∘
(Fig. 12). Nearly 75 % of the total annual wave energy is from the
direction between 245 and 270∘. At the study location, the
inclination of the coast is 17∘ to the west with respect to true
north. Depth contours appear as almost parallel with the 10 m contour
occurring at an average distance of 3.5 km from the coast. The wave
direction of 253∘ corresponds to the waves approaching parallel to
the coastline. Hence, due to refraction, most of the waves are approaching
the measurement location at 9 m water depth in a narrow range of 25∘
indicating that the wave directional scatter of the energy is less in the
nearshore waters. The high wave power (> 10 kW m-1) in shallow
waters along the west coast of India is due to the southwesterly
(250–270∘) waves and occurred during the monsoon period (Sanil Kumar
et al., 2013).
Seasonal and annual mean wave power from 1979 to 2015 at 30 m water
depth estimated based on ERA-I significant wave height and wave period data
Percentage of waves in different wave power ranges along with
average significant wave height, average energy period and average wave power
in different years and in different groups.
The above analysis using measured and reanalysis data indicates the seasonal
and interannual variations in wave power. Even though the marine environment
off the
west coast of India is not severe like the conditions in the Gulf of Mexico
and the North Sea (Arinaga and Cheung, 2012), during the monsoon period
significant wave height in the study area reaches a maximum of 5 m. At 9 m
water depth, the wave energy is concentrated in the classes over a range of
0.5–1 m with respect to Hs and between 6 and 10 s with respect
to the Te, with an annual occurrence of 31.38 % (approximately
114 days in a year). The global study by Arinaga and Cheung (2012) reported
very high monthly median wave power (∼ 72 kW m-1) in the Arabian
Sea in July, whereas, based on measured data, the median wave power during
July at 9 m water depth is 16.7 kW m-1. Anoop et al. (2015) have
shown that the intensity of waves in the Arabian Sea is higher (average wave
height ∼ 3 to 3.5 m) on the western side than that (∼ 2 to
2.5 m) on the eastern side during monsoon season as a result of the strong
southwesterly winds.
The wave power during the monsoon is 74–90 % of the annual wave power in
different years. Sanil Kumar et al. (2013) reported that along the west coast
of India, 83–85 % of the annual wave power is during the monsoon period
and the mean wave power is also high (15.5–19.3 kW m-1) during the
monsoon. Sanil Kumar and Anoop (2015) observed that along the western shelf
seas of India, most of the wave power is available during the monsoon period
when the availability of solar power is less due to cloud cover; and during
the non-monsoon periods, the availability of solar power is high when the
wave power is less. Hence, it would be ideal to build a combined wave and
solar power plant at the location studied.
Hovmöller diagram of the distribution of wave power with significant
wave height and wave direction at 9 m water depth from 2009 to
2012.
During the pre-monsoon period, the wave power is 9 to 17 % of the annual
wave power and the wave power during the post-monsoon period is 6 to 11 %
of the annual wave power in different years. The strong seasonality observed
in the wave power is similar to the variations observed in significant wave
height along the eastern Arabian Sea (Shanas and Sanil Kumar, 2014; Anoop et
al., 2015). Seasonal variability in wave parameters is observed in most of
the oceans (Portilla et al., 2013; McArthur and Brekken, 2010; Rusu, 2014;
Rusu and Onea, 2015). Even though high seasonal variability of wave power
(1–19.7 kW m-1) is observed in the study area, the variability is
less than the seasonal variability observed in the North Atlantic. Monthly
mean wave power in the North Atlantic varied from ∼ 10 kW m-1 in
July to ∼ 90 kW m-1 in January with an annual mean value of
∼ 45 kW m-1 (Barstow et al., 2008). Along the east coast of the
United States, the wave power resource tends to be much larger in the winter
(50 kW m-1) than in the summer (10 kW m-1) (Sierra et al.,
2013). A clear analogy can be seen between the high seasonal variability of
wave power along the central west coast of India and that along the European
shelf seas and the east coast of the United States.
Sanil Kumar and Anoop (2015) observed that the annual average wave power is
relatively high (∼ 12 kW m-1) in the central Arabian Sea and off
the southern tip of India and the average annual wave power along the western
shelf seas of India is 7.9–11.3 kW m-1. In the Southern Hemisphere,
the maximum annual mean wave power is ∼ 125 kW m-1 near
48∘ S, 94∘ E, southwest of Australia (Barstow et al.,
2008); and in the Northern Hemisphere, the annual mean wave power south of
Iceland (Barstow et al., 2008) exceeds 80 kW m-1 at around
56∘ N, 19∘ W. Averaged over years, offshore wave power
levels in the range of 30–100 kW m-1 are found at latitudes
40–50∘; and less power levels further north and south as well as in
most tropical waters have an average wave power level of below
20 kW m-1 (Falnes, 2007).
The ratio of the annual maximum significant wave height to the annual average
significant wave height is a measure for the feasibility of the energy
project (Barstow et al., 2008). The annual mean wave height determines the
annual mean wave power availability, whereas the annual maximum significant
wave height determines the design parameter for the wave power plant and
influences the investment cost. The ratio of the annual maximum significant
wave height to the annual mean significant wave height at 9 m water depth
varied from 3.3 to 4.2 in different years. Locations with low values of this
ratio favor setting up the wave energy plant and high values of the ratio
will lead to large investment cost (Barstow et al., 2008). High values for
the ratio of the annual maximum significant wave height to the annual mean
significant wave height are observed in locations affected by tropical
cyclones. The wave characteristics in the open ocean vary significantly if
the area is frequented by tropical cyclones and storms. In such areas, the
wave energy converters are to be designed for very high waves and will lead
to large investment costs and can lead to economic impacts in case of
failure. The examination of wave data at 30 m water depth during 1979 to
2015 shows that the interannual variations in the annual mean Hs
are less than 6 % and large variations in wave characteristics are not
observed in the study area. During 1979 to 2015, the interannual variations
in annual mean wave power at 30 m water depth are within 20 %.
Concluding remarks
The temporal and spatial variability of the wave power in the nearshore
waters of the eastern Arabian Sea are examined based on data collected at
three locations. At 9 m water depth, the wave power is more than
10 kW m-1 during 17–22 % of the time in a year and the mean wave
power during June–August measures more than 12 kW m-1. During the
non-monsoon period, the mean monthly wave power is less than 5 kW m-1
in all years. The attenuation in wave height is 15 % from 30 to 9 m and
5 % from 9 to 5 m, but the wave power available at 9 m water depth is
10 to 27 % less than that at 30 m and the wave power available at 5 m
water depth is 20 to 23 % less than that at 9 m. The wave power
estimated based on the ERA-I data are lower than the value estimated from the
measured data at 30 m water depth for high values (> 20 kW m-1)
with a bias of 3 kW m-1. At 9 m
water depth, during 52 % of the time, peak wave period is more than 12 s
with an average value of 14.3 s and during the same period, the average
value of energy period is only 8.8 s and hence estimating wave power based
on peak wave period will lead to large overestimation. The interannual
variations in annual mean wave power (at 30 m water depth) during 1979 to
2015 is within 20 % and large changes are not observed. The spread of
incoming wave directions is more concentrated within a narrow band
(∼ 25∘) at the shallower water depths due to refraction and is
advantageous for the capture of energy. The wave power estimation based on
bulk wave parameters obtained either from measurements, numerical modeling or
reanalysis data (ERA-I) will provide an approximate estimate of wave power at
a location and can only be used as a preliminary estimate. The wave power
estimate presented in this paper based on the wave spectrum from the measured
wave data can be used for planning wave energy converters.
Data availability
The measured wave data used in the study can be requested from the
corresponding author for joint research work. The long-term data on
significant wave height and wave period are from the ERA-Interim global
atmospheric reanalysis data set of the ECMWF and are available at
http://www.ecmwf.int/en/research/climate-reanalysis/era-interim (Dee et
al., 2011).
Acknowledgements
Director, CSIR-NIO, Goa, provided facilities to carry out the study. The
Council of Scientific and Industrial Research, New Delhi, funded the research
program. Shri Jai Singh, Technical Officer, CSIR-NIO, assisted in the data
analysis. This work forms part of the PhD thesis of the first author and the
CSIR-NIO contribution number is 5969. The
topical editor, M. Salzmann, thanks two anonymous referees for their help in
evaluating this paper.
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