**C.3 Exploratory Data Analysis**

**7.1 Locations of wave measuring buoys**

TABLE7.1: Descriptive statistics of the available data set

Last Location Water Date Range Observations Coverage Missing Missing Effective Record

Depth (m) (%) Days (%) Month (%) Length (years)

Cairns 16°26’18"S 145°25’45"E

12 4/05/1975

-31/12/2019

397,302 95.31 9.02 2.24 42.56

Townsville 19°05’44"S 147°02’08"E

17 20/11/1975

-31/12/2019

387,310 89.54 8.48 1.89 39.50

Mackay 21°03’39"S 149°09’17"E

12 19/09/1975

-31/01/2018

312,003 71.13 14.00 6.29 30.14

Hay Point 21°09’47"S 149°11’14"E

10 24/03/1977

-31/12/2019

411,304 87.02 16.10 13.80 37.22

Emu Park 23°10’59"S 151°02’34"E

19 24/07/1996

-31/12/2019

342,220 94.04 3.18 0.36 22.04

Mooloolaba 26°20’23"S 153°06’31"E

32 20/04/2000

-31/12/2019

322,988 93.52 3.70 2.53 18.42

Brisbane 27°17’32"S 153°22’44"E

70 31/10/1976

-30/06/2019

398,682 94.37 6.89 0.20 40.27

Gold Coast 27°34’45"S 153°15’56"E

17 21/02/1987

-31/12/2019

410,306 89.10 4.58 0.00 29.28

Tweed Heads 28°06’24"S 153°20’45"E

22 13/01/1995

-30/06/2019

371,006 86.65 0.72 0.00 21.20

Byron Bay 28°52’14"S 153°41’39"E

62 14/10/1976

-31/12/2018

245,042 77.77 17.00 4.73 32.83

Coffs Harbour 30°21’45"S 153°16’09"E

72 26/05/1976

-31/12/2018

273,445 86.90 10.50 1.56 37.02

Crowdy Head 31°48’50"S 152°51’22"E

79 10/10/1985

-31/12/2018

254,542 87.01 9.01 0.50 28.91

Sydney 33°46’26"S 151°24’42"E

90 3/03/1992

-31/12/2018

199,534 84.37 7.24 1.86 22.64

Port Kembla 34°28’35"S 151°01’33"E

80 7/02/1974

-31/12/2018

272,974 85.50 11.80 3.53 38.39

Batemans Bay 35°42’11"S 150°20’38"E

73 27/05/1986

-31/12/2018

257,469 89.70 7.65 1.02 29.24

Eden 37°15’57"S

150°11’36"E

100 08/02/1978

-31/12/2018

261,554 84.16 11.00 3.26 34.42

Cape du Couedic 36°04’12"S 136°36’36"E

80 29/11/2000

-31/12/2019

688,623 89.34 7.43 3.04 17.05

Cape Sorell 42°07’12"S 145°01’48"E

100 7/01/1998

-31/12/2019

658,752 94.11 4.18 0.76 20.69

Our goal is to investigate and compare long-term trends in the wave climate along Australia’s eastern and southeastern coast. For this, we use 18 wave rider buoys, of which nine are lo-cated in Queensland, seven in NSW and one each in South Australia and Tasmania. Figure 7.1 provides an overview of the particular locations of the buoys used in this work. Table 7.1 presents a detailed overview of the wave buoy locations, information about their water depths and information about the dataset, including the date range and coverage.

The data for the buoys in Queensland are publicly available and have been downloaded from the Open Data Portal of the Queensland Government. The data on the buoys of Cape du Couedic and Cape Sorell have been downloaded from the Australian Ocean Data Network.

The stations in NSW are recorded by the NSW Office of Environment and Heritage. We would like to thank Mark Kulmar and the Manly Hydraulics Laboratory for providing us with the data on these buoys.

We have chosen this particular network of wave buoys based on data availability ranging from 17 effective record years (product of record years and coverage) for Cape du Couedic in Tasmania and 42 years for Cairns in Far North Queensland. Data have been captured by the waverider buoys with various minimal intervals ranging from 12 and 6 hours in the 1970s and

1980s, to hourly or half-hourly intervals for later periods. Since 1984, all wave buoys in NSW have captured data at 1-hour intervals. For Queensland, 1-hour intervals have been recorded in our dataset since 1991 in Gold Coast and Townsville, whereas by 1994, all stations are record in this frequency. For the two buoys in South Australia and Tasmania, we even have partially minimum intervals of 15 min, which is why we have more than 650,000 recorded observations – considerably more than for the other stations. Data quality and coverage varies among the locations from 78% in Byron Bay to 95% in Cairns. Figures 7.9 and 7.10 in Appendix G provide a graphical analysis of the gaps and missing data for all buoys over time.

To avoid distorting seasonal effects for our trend analysis and the Laplacian embedding in the following section, we restrict our analysis to full record years at the beginning and end of our data sets. Thus, for example, we limit our analysis to the period January 1977 and December 2018 for Brisbane. Two exceptions to this rule are the buoys in Mackay and Port Kembla. In Mackay, the beginning and end of our records have multiple missing months in a row, which is why we restrict the analysis to the year range of 1978 to 2016. In Port Kembla, we have multiple missing months at the beginning of the record and thus start our analysis in 1976.

**7.2.1** **Characterization of Parameters**

Ocean waves are produced by wind blowing over the sea surface. The surface is composed of various random waves with different lengths, periods and directions. The distribution of wave energy with variations in the wave frequency and wave length on the sea surface is described by the wave spectrum (Stewart 2008). A not fully developed sea state is commonly represented by the spectrum that resulted from research by Hasselmann et al. (1973) in the Joint North Sea Wave Observation Project (JONSWAP). According to this, the JONSWAP spectrum can be described as:

S(*ω*) = ^{αg}

2

*ω*^{5} e^{[−}^{5}^{4}^{(}^{ωp}^{ω}^{)}^{4}^{]}*γ*^{e}

[−(* _{ω}*−

*)*

_{ωp}^{2}2σ2

*ω*2p

]

, (7.1)

*α*=0.076(^{U}

102

Fg)^{0.22}, (7.1a)

*ω*_{p}=22( ^{g}

2

U10F)^{1}^{3}, (7.1b)

*γ*=3.3, (7.1c)

*σ* =

(0.07 *ω* ≤*ω*p

0.09 *ω* >*ω*_{p}

, (7.1d)

whereS(*ω*)is the spectral variance density,*ω*_{p}denotes the peak frequency,gthe gravitational
acceleration,U_{10}the wind speed at a height of 10 m,Fis the distance from a lee shore (fetch), or
the distance over which the wind blows with constant velocity and*ω*is the wave component
frequency. Moreover,*γ*is called the peak enhancement factor.^{3}The spectral moments can then
be used to define other characteristics of a sea-state, such as the significant wave height and

3 Note: The spectral shape of the JONSWAP is an extension of the Pierson-Moskowitz (Pierson and Moskowitz
1964) spectrum multiplied by peak enhancement factor*γ*to allow for a more pronounced peak in the spectrum.

average zero-crossing period. Thereby, the nth-order moment,m_{n}, of the spectrum is defined
as:

mn=

Z _{inf}

0 S(*ω*)*ω*^{n}dω. (7.2)

The wave height can be computed from the zero-order moment,m_{0}, as follows:

H_{m0} =4√

m_{0}. (7.3)

H_{m0}is similar to the significant wave height represented as the average height of the highest
one-third of waves, which is another commonly used method in wave buoy records. Given our
data, we will use the latter definition and refer to the significant wave height asH_{s}throughout
the manuscript. Moreover, one can further define the mean zero-crossing period of the waves
Tz as:

Tz =
rm_{0}

m_{2}. (7.4)

Given the JONSWAP spectrum with a peak enhancement factor of*γ* = 3.3, one can relate T_{z}
to two other commonly used measures of the wave period, namely the peak period, T_{p} (the
wave period of those waves producing the most energy in a wave record) and the wave energy
period,T_{e} (defined as the ratio of the first negative moment to the zero-order moment of the
wave spectrum(^{m}_{m}^{−}^{1}

0 )), as follows (Pecher and Kofoed 2017):

1.12T_{e}=1.29T_{z} = T_{p}. (7.5)

Consequently, omnidirectional WP in deep water can be estimated from the spectral parame-ters defined above as:

WP= ^{pg}

64πT_{e}(H_{s})^{2}_{.} _{(7.6)}

This is the rate at which wave energy is transmitted in the direction of wave propagation.

It is normally expressed in kilowatts per meter of wave crest length, where WP is expressed
in kW/m of the wave front, p is the sea water density (1025.9 kg/m^{3} at 15 °C) and g is the
gravitational acceleration (9.8m/s^{2}). We will useTpfor calculating WP for our further analysis.

**7.2.2** **Descriptive Statistics**

Table 7.2 presents a full summary of the descriptive statistics for the WP of our 18 locations.

Wave buoys in Queensland exhibit a mean significant WP ranging from between 0.63 kW/m
in Cairns to 13.51 kW/m in Brisbane. The WP in NSW seems to be more grouped together in
the range of 12.93 to 14.12 kW/m with the exception of Batemans Bay with a reduced mean
WP of 10.42 kW/m.^{4}The mean WP in Cape du Couedic and Cape Sorell is considerably higher
than for the buoys in NSW and Queensland.^{5} Similar statements can be made for the other
parameters. There seems to be a general tendency of buoys in NSW being grouped closer
to-gether than in Queensland when considering the median, the 90th and 99th percentiles, as well
as the maximum. Additionally, this can be seen graphically from the exceedance Hs plotted in
Figure 7.2, and it seems to hold true throughout the set of exceedance probabilities. Moreover,
all stations exhibit a positive skewness and high excess kurtosis.

4 The reduced wave climate can be explained by coastal orientation and land-mass sheltering from Victoria, Tas-mania and New Zealand (Coghlan et al. 2011).

5 This can be explained by wind-waves generated by extra-tropical cyclones of the Southern Ocean. These waves can travel long distances without loosing much of its energy until shoaling near the coast of Western Australia and the southern Tip of Tasmania (McInnes et al. 2016).