An assessment
of extreme wave characteristics during the design of marine facilities not
only helps to ensure their safety but also assess the economic aspects. In
this study, return levels of significant wave height (

Coastal zones are relatively dynamic compared to the rest of the regions due to numerous natural as well as anthropogenic activities. Events such as extreme waves, storm surges and coastal flooding cause large catastrophes in the coastal region. The long-term (climate) behavior of sea state variables can be studied using non-stationary multivariate models that represent the time dependence of the variables (Solari and Losada, 2011). Various marine activities such as the design of coastal and offshore facilities, planning of harbor operations and ship design require detailed assessment of wave characteristics with certain return periods (Caires and Sterl, 2005; Menéndez et al., 2009; Goda et al., 2010). Generally, extreme value theory (EVT) is used for the determination of return levels by adopting a statistical analysis of historic time series of wave heights obtained from various sources such as in situ buoy measurements (e.g., Soares and Scotto, 2004; Méndez et al., 2008; Viselli et al., 2015), satellite data (e.g., Alves et al., 2003; Izaguirre et al., 2010), and hindcasted or reanalysis data by numerical models (e.g., Goda et al., 1993; Caires and Sterl, 2005; Teena et al., 2012; Jonathan et al., 2014). EVT consists of two types of distributions, viz. the generalized extreme value (GEV) distribution family which includes the Gumbel, Fréchet and Weibull distributions (Gumbel, 1958; Katz et al., 2002) and generalized Pareto distribution (GPD) which incorporates the peak over threshold (POT) approach (Pickands, 1975; Coles et al., 2001).

GEV distribution by annual maxima (AM) observations (Goda, 1992) is one of
the widely used methods in the EVT analysis. The main
difficulty with using this method is the unavailability of reliable
observations at a location of interest. To overcome the data scarcity,
two different alternatives have been used by various authors: (i) the initial
distribution method (IDM), in which all the data are
used (Alves and Young, 2003); and (ii) the

The most reliable source of ocean wave data is buoy measurements, and it can be
used for EVT analysis (Panchang et al., 1999). In this paper, data from a directional
Waverider buoy located in the central western shelf of India are used.
Seasonality is one of the important aspects of climate data, and, therefore,
it should be incorporated in the EVT analysis of waves, especially in a region such as
the Arabian Sea. Seasonal analysis of the extremes helps in the planning of
short-term marine activities such as offshore explorations and maintenance of
coastal facilities. In the present paper, the EVT analysis is carried out by
following both the GEV and GPD methods considering wind-sea, swell and total
significant wave height (

The paper is organized as follows. Section 2 deals with the data and
methodology used in the analysis. It also presents the threshold selection
adopted in the study, and Sect. 3 explains the results obtained in the
analysis, categorized into seasons using total

Data used in the analysis are from a Datawell directional Waverider buoy
deployed off Honnavar (14.304

The

The comparison of 50- and 100-year significant wave height return levels based on buoy, ERA-Interim shallow and ERA-Interim deep data at 6 h intervals along with data statistical parameters.

EVT analysis is carried out by following the GEV distribution model and the POT method in
which exceedance over a reliable threshold wave height can be fit into GPD.
In the POT method, distribution of excess,

Different goodness of fit tests used for selecting threshold values
of POT analysis.

Time series plot of the significant wave height measured by buoy and from ERA-Interim data at shallow and deep water.

The analysis is carried out by using the wind-sea, swell and total

Estimated shape parameters for different seasonal data with
different sampling intervals used in the

Table showing different parameters and corresponding RMSEs of data and the estimated CDF used during each data series analysis.

Typical

Figure corresponding to the full-year analysis.

To study the uncertainties related to the length of the observation, we extracted 3, 6, 12 and 24 h data series from the half-hourly original data and carried out EVT analysis. Since the wave climate in the study location is strongly characterized by the prevailing seasonal behavior of wind system, we took further consideration of uncertainties related to a seasonal aspect of wave climate by extracting three seasonal data sets, viz. pre-monsoon (FMAM), monsoon (JJAS) and post-monsoon (ONDJ) seasons.

The major drawback of EVT analysis using the block maxima method, especially the annual maxima, is that it does not consider the significant amount of observations which are closely related to storm features of the data set. Those omissions of observations would cause significant variations in the final results of EVT analysis, especially in the cases where EVT analysis is performed for a very limited data set. EVT is based on the assumption that the observations under consideration are independent and identically distributed (Coles et al., 2001). We can expect identical status of ocean wave observations for a large extent. Since the POT approach resamples the data over a threshold value, making identical and independent observations is a tedious task. A suitable combination of threshold and minimum separation time between the resampled observations must be taken into account to establish independence among the observations.

The average duration of tropical storms in the Arabian Sea is 2–3 days (Shaji et al., 2014). Therefore, in the present analysis, we fixed a minimum of 48 h of separation time in between two consecutive storm peaks to ensure the independence of the data points for the analysis. Then, we selected a tentative threshold value in such a way as to ensure the presence of at least 15 peak values per year on average. This resulted in at least 120 data points in each sub-data sets used for the seasonal analysis. The resulting data series are used in further POT analysis. Further adjustment of the threshold is carried out by sample mean excess (SME) plots and parameter stability plots (PS plot). From these plots, we selected four probable thresholds and fitted the corresponding GPD. A final threshold value is chosen by analyzing results obtained in different goodness of fit (GOF) tests such as the Kolmogorov–Smirnov (KS) test, Anderson–Darling (AD) test and Cramér–von Mises (CM) test (Stephens, 1974; Choulakian and Stephens, 2001).

The distributions used in the analysis are validated using graphical tools
such as quantile–quantile (

Estimated return values corresponding to different seasons using
total wave height (

Same as in Fig. 4 but corresponding to the pre-monsoon season.

Same as in Fig. 4 but corresponding to the monsoon season.

The mean wave climate at the study location is characterized by an annual
mean

Return levels estimated by the GEV model using total, wind-sea and swell data for different block maxima series.

Same as in Fig. 4 but corresponding to the post-monsoon season.

Return levels of significant wave heights for different return periods based on buoy data (2008–2016), ERA-Interim shallow water data and ERA-Interim deep water data (1979–2016) at 6 h intervals by the GEV model using annual maxima series.

Here, we considered full-year data series without dealing with seasonality,
and both the GEV and GPD are used in the analysis. Initially, a range of
thresholds from 2.5 to 3.4 m was selected, and further adjustment of the
threshold is carried out by analyzing the GOF test results. Table 2 shows the
selected thresholds and the corresponding GOF test results for each series in
the full-year data analysis. It is clear that the selected thresholds are in
good agreement with the GOF test results. Both the KS test and CM test give a

Density plots showing the probability for different wave height
class. Total, wind-sea and swell

Table showing the results of the case study. The standard deviations (SDs) of each data series considered are provided, and percentage differences among the SDs of each series with parent series (S0) are given in the brackets. The percentage difference in the corresponding return level estimation is also shown in the brackets of the respective return periods.

The data from February to May constitute the pre-monsoon data set.
Pre-monsoon is the calmest season in the study location, with a maximum and
an average

The monsoon season data set covers observations from June to September, and
this season is characterized by rough wave climate at the study location.

The post-monsoon season constitutes data from the October to January months
of the year, and the observed maximum

In this section, we relied on the GEV method based on block maxima. For that
purpose, we extracted total, wind-sea and swell

Return levels of significant wave heights for different return periods based on ERA-Interim shallow water data in different block years by the GEV model using annual maxima series.

We performed a separate analysis of the annual maxima series to get insight
into the abnormal results observed for wind-sea data series. Here, we
considered four unique series of different lengths by taking annual maxima
observations from 2008 to 2016; that is, the first series (S1) consists of
five data points (2008–2012) and second series (S2) consists of six data
points (2008–2013) and so on. The density plots showing the probability for
different wave height class are presented in Fig. 9 along with the
corresponding GPD fit. We calculated the standard deviation for each series
and the percentage difference between each series and the parent series (S0).
The result shows that return levels are positively correlated with standard
deviation (Table 6).
In the case of the total

An analysis is carried out to check uncertainties in return level estimation
related to the length of the wave record. From the 0.5 h buoy-measured data,
data at 6 h intervals are extracted and used for the analysis, and the
return levels obtained by using 6 h measured buoy data are compared with the
return level obtained from the 6 h ERA-Interim data at shallow and deep
locations (Fig. 8). The 6-hourly ERA-Interim reanalysis 38-year data
(1979–2016) are used in this analysis. Buoy data consist of 11 479 data
points, and ERA-Interim data consist of 55 520 data points (Table 1). The
highest observed

Variation of the

We have examined the difference in the return level of

The long-term and decadal trend of wave climate in the different parts of
major oceans is studied (Young et al., 2011). We have examined the trend in

The percentage of time of the waves in the shallow, intermediate and deep water regime in different years along with the mean wave period and mean peak wave period.

The relative water depth based on the spectral peak period (

Wave rose plots from March 2008 to February 2016 based on the measured buoy data and the ERA-Interim reanalysis data at shallow and deep water locations.

Long-term statistical analysis of extreme waves is carried out based on GEV
and GPD models using measured buoy data from March 2008 to February 2016 and
the ERA-Interim data from 1979 to 2016. Return levels are calculated for
resultant, wind-sea and swell

Long-term statistics of wind-sea and swell data are calculated by the GEV
model following block maxima and the

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 wind speed are from the ERA-Interim global atmospheric reanalysis data set of the ECMWF
and are available at

The authors declare that they have no conflict of interest.

The director of the CSIR–National Institute of Oceanography, Goa, provided the facilities to carry out the study. 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 is CSIR–NIO contribution number 6103 under the institutional project MLP1701. We thank the editor Mauricio Gonzalez and the two anonymous referees for their suggestions for improving the manuscript.Edited by: Mauricio Gonzalez Reviewed by: two anonymous referees