Cross-shore profile survey on beaches has been conducted weekly from 1999 at the Omotehama Coast, Japan, and data of shoreline position was stored during 14 years. The shoreline position was influenced by many kinds of impacts, such as daily waves, typhoon in several days, seasonal changes of sea condition. Additionally, long-period variation was laid in the measurement of shoreline change. The long-period variation might characterize the trend of shoreline change. However, characteristics of the long-period variation have not been made clear because the measurement with a sufficient period is necessary to investigate them. The estimation of a coastal trend whether it will be erosive or accretive in a long term is important to discuss coastal management. In this research, time-frequency analysis of the shoreline change was conducted by Hilbert-Huang transform (Huang et al., 1998). By Empirical Mode Decomposition (EMD), 14-year shoreline position data was decomposed into only eight Intrinsic Mode Functions (IMFs) from a short period to a long period. The IMFs from 6th to 9threpresented long-period components. Their mean periods calculated by an instantaneous frequencyare more than 1-year. Variations of amplitude of these components are from 10 to 20 m although yearly averaged variation of shoreline position is from 30 to 40m. The contribution of more than 1-year period components was evaluated by the variance, and its ratio was more than 30% in the measurement. The result suggests that the long-period components have much influence on the trend of long-term shoreline change

Kato, S.

Okabe, T.

Sawahara, N.

Hasanuddin University Repository

 91 
 
 
Proceedings of the 7th International Conference on Asian and Pacific Coasts 
(APAC 2013) Bali, Indonesia, September 24-26, 2013 
 
 
 
INFLUENCE OF LONG-PERIOD VARIATION ON SHORELINE CHANGE  
 
S. Kato 
1
, T. Okabe 
2
 and N. Sawahara 
3
 
 
 
ABSTRACT:Cross-shore profile survey on beaches has been conducted weekly from 1999 at the Omotehama Coast, 
Japan, and data of shoreline position was stored during 14 years. The shoreline position was influenced by many kinds 
of impacts, such as daily waves, typhoon in several days, seasonal changes of sea condition. Additionally, long-period 
variation was laid in the measurement of shoreline change. The long-period variation might characterize the trend of 
shoreline change. However, characteristics of the long-period variation have not been made clear because the 
measurement with a sufficient period is necessary to investigate them. The estimation of a coastal trend whether it will 
be erosive or accretive in a long term is important to discuss coastal management. In this research, time-frequency 
analysis of the shoreline change was conducted by Hilbert-Huang transform (Huang et al., 1998). By Empirical Mode 
Decomposition (EMD), 14-year shoreline position data was decomposed into only eight Intrinsic Mode Functions 
(IMFs) from a short period to a long period. The IMFs from 6thto 9threpresented long-period components. Their mean 
periods calculated by an instantaneous frequencyare more than 1-year. Variations of amplitude of these components are 
from 10 to 20 m although yearly averaged variation of shoreline position is from 30 to 40m. The contribution of more 
than 1-year period components was evaluated by the variance, and its ratio was more than 30% in the measurement. The 
result suggests that the long-period components have much influence on the trend of long-term shoreline change. 
 
Keywords:Shoreline change, long-period variation, time-frequency analysis, long-term trend. 
 
 
                                                 
1Department of Architecture and Civil Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka, Tempaku-cho, 
Toyohashi, Aichi, 441-8580, JAPAN 
2Department of Architecture and Civil Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka, Tempaku-cho, 
Toyohashi, Aichi, 441-8580, JAPAN 
3Sogo Sekisan Corporation, 1-11-19 Higashitenma, Kita-ku, Osaka, Osaka, 530-0044,JAPAN 
INTRODUCTION 
A shoreline position was influenced by many kinds 
of impacts, such as daily waves, typhoon in several days, 
seasonal changes of wave and tidal conditions. The 
shoreline position changes uninterruptedly. Then, the 
shoreline position can be variable over a wide range of 
different temporal scales (Stive et al, 2002). There are 
some cases in which a trend of erosion (recession of 
shoreline position) is indicated in a short term (e.g., 
several months and less than 1 year) although a trend of 
accretion (shoreline position forward to sea) is 
recognized by measured data in a long term (e.g., more 
than several years). Additionally, a presence of long-
period variation is occasionally perceived in the long-
term data. The long-period variation might play an 
important role to characterize the trend of a long-term 
shoreline change. It is important to grasp the trend of 
shoreline variation in an appropriate period for long-term 
coastal management, which is including a 
countermeasure for coastal erosions locally. It is, 
however, imprecise which periods of constitutional 
variations are important for the long-term coastal 
management and how much those variations have 
influence on the whole shoreline change in a field. 
Investigation and discussion with continuous beach 
monitoring are indispensable for the suitable and 
successful coastal management.  
The purpose of this research is to know the 
characteristics of a decadal shoreline change at the 
Omotehama Coast. Using the survey data, time-
frequency analysis of shoreline change is carried out. A 
detection of local and overall properties in time of 
shoreline change is attempted by Hilbert-Huang 
transform (Huang et al., 1998). The contribution of long-
period variations in the shoreline change is also 
investigated for the suitable coastal management. 
 
SUMMARY OF COASTAL SURVEY AND 
SHORELINE POSITION DATA  
Coastal survey was started on May, 1999, and has 
been continued even now at 3 locations (Takatsuka, 
Terasawa and Kojima) on the Omotehama Coast. The 
coast is facing the Pacific Ocean (Fig.1). The survey is 
carried out at almost every 1 week at low tide. The beach 
profile of a cross-shore section at each location is 
measured by the leveling from a bench mark installed on 
land to sea with 5 m interval. The shoreline position is 
estimated as a location of intersection of measured 
S. Kato, et al. 
92 
 
ground level with mean monthly-highest water level by 
linear interpolation of the measurement. The highest 
water level at this coast is 0.88m above Tokyo Bay mean 
sea level (Tokyo peil; T.P.). Data of shoreline position 
has been stored almost 14 years. In this research, 
shoreline position data at Terasawa was analyzed. At 
Terasawa, wave dissipating concrete blocks were 
installed on the middle of sandy beach. Waves reach the 
blocks in case of high tide and high wave conditions. 
The details of the coastal survey and survey locations 
were summarized in Aoki and Obata(2000) and 
Nagasaka et al.(2010). 
 
TEMPORAL CHARACTERISTICS OF 
SHORELINE POSITION  
Figure 2 shows a time series of shoreline position at 
Terasawa from May 1999 to December 2012. The 
shoreline position moved back (erosion) and forth 
(accretion) with a range of 30 ~ 40m annually. An 
annual pattern of shoreline change was erosion in 
summer and fall due to stormy waves, e.g., by typhoon, 
and gradual accumulation during winter to spring. The 
long-term trend of shoreline change indicates gradual 
accretion as shown by a dashed line which is a linear 
regression line of whole measured shoreline data. On the 
contrary, the different trends are appeared in case the 
data is divided into every 3 years (Fig. 3). The tendency 
seems to be almost constant in the period from 2000 to 
2002 (Fig. 3(a)). It means that the shoreline position was 
stable on the whole although it continued changing. But 
the erosive trend is appeared in the period from 2010 to 
2012 (Fig. 3(c)). It is difficult to guess the accumulative 
tendency in a long term from the recent 3 years. The 
different length of analyzed data will show us the 
different characteristics of coastal condition (tendency 
toward erosion or accretion).  
Coastal survey was conducted roughly every 1 week 
at low tide. But owing to weather and tidal conditions, it 
was carried out at irregular intervals from 2 to 10 days. 
The data at the irregular intervals is unsuited to data 
analysis such as Fourier transform. The data at regular 
intervals was made by means of spline interpolation. The 
statistical properties, such as mean, maximum, minimum 
and standard variation, of the interpolated data at regular 
intervals with 7 days are much similar to those of the 
surveyed data. The interpolated data was used in further 
analysis. 
 
 
Mikawa-Bay
0                 10km
Takatsuka
Terasawa
Kojima
Maisaka
Pacific Ocean
 
 
Fig.1 Location of surveys and nearest tide station on the 
Omotehama Coast, Japan 
 
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Fig.2 Shoreline change and a liner trend at Terasawa 
(1999~2012) 
 
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Terasawa
 
(a) 2000/01/01 ~ 2002/12/31 
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Terasawa
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Terasawa
 
(b) 2006/01/01 ~ 2008/12/31 
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Terasawa
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Terasawa
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2010/01 2011/01 2012/01
Terasawa
 
(c) 2010/01/01 ~ 2012/12/31 
Fig.3 Shoreline change and a linear trend in each 3 years 
 
Influence of Long-Period Variation on Shoreline Change  
 
93 
 
SUMMARY OF HILBERT-HUANG TRANSFORM 
Hilbert-Huang transform (HHT) proposed by Huang 
et al. (1998) mainly consists of empirical mode 
decomposition (EMD) and Hilbert transform (HT). The 
HHT makes possible to investigate variations of both 
frequency and amplitude on time axis, simultaneously. 
Firstly, an original data is decomposed into a finite 
number of intrinsic mode functions (IMF) and a residue 
by EMD. Each IMF is a narrow band, but has amplitude 
and frequency modulations. The residue is a trend or an 
average of the original data. Secondly, instantaneous 
frequencies and amplitudes are estimated in each IMF by 
HT. In case of a temporal data, the instantaneous 
frequency and amplitude are a function of time. 
Therefore, the amplitude can be expressed as a function 
of time and frequency. The amplitude is called as Hilbert 
amplitude spectrum, or simply, Hilbert spectrum. By the 
Hilbert spectrum, time-frequency properties of the 
original data can be investigated. The details of HHT are 
found in Huang et al. (1998) and Huang and Shen (2005). 
The R package for EMD (Kim and Oh, 2009) is used for 
data analysis in this research. 
 
FREQUENCY CHARACTERISTICS OF 
SHORELINE CHANGE  
Figure 4 shows the IMFs derived from the shoreline 
position data at Terasawa. The original data was 
decomposed into only 9 IMFs from a short period to a 
long period. The envelope of each IMF is drawn by a 
spline function to catch amplitude modulation easily. 
Frequency modulation is also confirmed in each IMF. 
The Hilbert spectrum is displayed together with the time 
series of the shoreline change and the rate of that per day 
in Fig. 5. The color of dark blue indicates high energy 
(large instantaneous amplitude) of an IMF. Long-period 
components more than 2 years exist widely with energy 
fluctuations, whereas variations less than semi-annual 
period appear intermittently. It is also easy to know that 
variations with various periods are comprised locally in 
time in the shoreline change. Distinctively Sudden 
changes, which areerosion over 2m/day, of the shoreline 
position are marked with labels, (i) ~ (vi) in the middle 
of Fig.5. In the bottom figure (Hilbert spectrum), dark 
blue symbols are shown in the short-period range at the 
corresponding time of the sudden changes except for (iii). 
On the other hand, a period of variations at (iii) is longer 
than others. It is around 1 year .The large accretion at 
(iii) was one of distinctive change as same as others. It is 
found that the Hilbert spectrum can detect local shoreline 
changes in terms of time. The ability of local property’s 
detection is an advantage of HHT as compared with the 
analysis by Fourier transform. Figure 6 shows the time 
series of daily mean water level and Hilbert spectrum at 
the nearest tide station which is at Maisaka (see Fig.1). 
The variation with 1-year period is a dominant 
component in the mean water level. However, high 
energy of variations is confirmed in the short-period 
range occasionally. Some of these are corresponding to 
the shoreline change at (ii), (iv) ~ (vi). Then, it is 
supposed that mean water level variations with a short 
period less 2 or 3 months has an impact on the 
remarkable retreat of shoreline. 
 
CONTRIBUTION OF LONG-PERIOD 
VARIATION IN SHORELINE CHANGE 
Figure 7 provides us with a Fourier spectrum and a 
marginal Hilbert spectrum of the shoreline data. The 
spectral profiles are smoothed by a 3-point triangle filter. 
The marginal Hilbert spectrum is measured by 
integrating Hilbert spectrum (Fig.5) over the time at each 
frequency, and the spectrum is increased the quantity by 
ten times to compare with the Fourier spectrum easily. 
While the Fourier spectrum describes the presence of a 
monochromatic wave component with a certain 
frequency over the whole time span of the data, the 
marginal Hilbert spectrum can give us a total amount of 
3
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date
 
Fig.4 Original data, extracted IMFs by EMD and residue 
of shoreline data 
 
S. Kato, et al. 
94 
 
the energy contribution from each frequency.There are 
very clear peaks at the period slightly smaller than 1 year 
in both the Fourier spectrum and the marginal Hilbert 
spectrum. In the marginal Hilbert spectrum, this peak 
means strong and local variations in time, such as (iii). It 
is suggested that the peak in the Fourier spectrum 
indicates an annual variation of the shoreline positions. 
However, it is difficult to grasp its variation clearly in 
the temporal shoreline change. The highest density is 
between 2- and 3-year periods in both spectra. The 7th, 
8thand 9thIMFs in Fig.4 correspond to the long-period 
variations more than 2 years. The amplitude of these 
modes modulates with time.The variations of amplitude 
of these modes are from 10 to 20 m although annual 
variation of shoreline position is from 30 to 40 m.  
Figure 8 shows decomposed shoreline changes with 
certain period ranges by the Fourier transform. The 
corresponding periods are more than 3 years, from 2 to 3 
years, from 1 to 2 years, from 0.5 to 1 years and less than 
0.5 years from top to bottom. The bottom figure shows a 
trend (a linear regression line) of the original shoreline 
data. The range of fluctuations more than 1-year period 
components is much similar to that of the 6th~ 9thIMFs. 
Variances of each component in Fig.8 are calculated in 
Fig.9. The sum of contribution of more than 1-year 
period components is more than 30 % in the total 
variation of the shoreline position. Then, to know and to 
estimate these long-period variations appropriately will 
be possible to make a suitable plan for a long-term 
coastal management. 
Frequency (Cycle/day)
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4 2 1 0.5 0.17
Period (year)
Fourier Spectrum
marginal Hilbert Spectrum (x10)
 
Fig.7 Fourier and marginal Hilbert spectrum of shoreline 
change  
 
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T > 3yrs
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1999/01 2001/01 2003/01 2005/01 2007/01 2009/01 2011/01
linear trend
date  
Fig.8 Decomposed components by Fourier transform and 
a linear trend of shoreline change 
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0.17
0.50
1.00
2.00
3.00
4.00
(i)  (ii)           (iii)                     (iv)        (v)            (vi)  
 
Fig.5 Shoreline change, rate of change per day and its 
Hilbert spectrum 
 
-0
.2
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.2
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.6
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In
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p
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.(
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a
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1999/01 2002/01 2005/01 2008/01 2011/01
0.17
0.50
1.00
2.00
 
Fig.6 Dailymeanwater level and its Hilbert spectrum 
Influence of Long-Period Variation on Shoreline Change  
 
95 
 
 
CONCLUSIONS  
This research described the characteristics of the 
shoreline change during 14 years at the Omotehama 
Coast. Depending on a temporal scale of analyzed data, 
the long-term tendency of the shoreline changes seems to 
be different. It is difficult to judge the tendency of 
erosion or accretion by the data with limited temporal 
length. 
By the Hilbert-Huang transform (HHT), the time-
frequency analysis was conducted to investigate the 
characteristics of frequencies buried in the shoreline 
change. The variations with a short period and high 
energy were detected in the Hilbert spectrum. The 
correspondence between the daily mean water level and 
the shoreline change in the viewpoint of local frequency 
property was also confirmed in the Hilbert spectrum. On 
the other hand, long-period variations more than 2 years 
with an energy fluctuation were identified. 
Finally, the contribution of long-period variations was 
estimated. As the more than 1-year period components 
have a significant fluctuation compared with the 
shoreline change by the EMD decomposition and the 
Hilbert spectrum, the importance of these components 
were confirmed in both the Fourier spectrum and the 
marginal Hilbert spectrum. The contribution of the long-
period variations was estimated using the variance. It 
was indicated that the contribution of more than 1-year  
 
 
 
 
 
 
 
 
 
 
 
 
 
period components is more than 30 % in the total 
variation of the shoreline change at the Omotehama 
Coast. 
 
ACKNOWLEDGEMENTS 
The coastal survey at the Omotehama Coast was 
started by Prof. Shin-ichi Aoki, Osaka University. And 
this survey has been continued owing to the cooperation 
by the members of Coastal Engineering Laboratory, 
Toyohashi University of Technology. The author would 
like to thank to them. 
 
 
REFERENCES 
Aoki, S and Obata, H. (2000). Influences of Unusual 
High Sea Level on Short-Term Variations of 
Shoreline and Foreshore Profile, Proceedings of 
Coastal Engineering, JSCE, Vol.47, 586-590. (in 
Japanese) 
Huang, N. E. and Shen, S. S. P. (2005).Hilbert-Huang 
Transform and Its Applications, Interdisciplinary 
Mathematical Sciences – Vol.5, World Scientific, 
311p. 
Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. 
H., Zheng, Q., Yen, N.-C., Tung, C. C. and Liu, H. H. 
(1998). The Empirical Mode Decomposition and 
Hilbert Spectrum for Nonlinear and Nonstationary 
Time Series Analysis, Proceedings of the Royal 
Society London A., 454, 903-995. 
Kim, D and Oh, H-S., (2009). EMD: A Package for 
Empirical Mode Decomposition and Hilbert 
Spectrum, The R Journal, Vol. 1/1, 40-46. 
Nagasaka, K., Aoki, S.,  Kato, S., Okabe, T. and Kataoka, 
M. (2010). Characteristics of Beach Profile Change 
at a Sandy Coast, Journal of JSCE, Ser. B2 (Coastal 
Engineering), Vol.66, 566-570. (in Japanese) 
Stive, M. J. F, Aarninkhof, S. G. J., Hamm, J., Hanson, 
H., Larson, M.,Wijnberg, K. M., Nicholls, R. J. and 
Capobianco, M. (2002).Variability of Shore and 
Shoreline Evolution, Coastal Eng. 47, pp.211-235. 
 
T > 3yrs 2 < T < 3yrs 1 < T < 2yrs 0.5 < T < 1yr T < 0.5yr
R
a
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V
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0
1
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3
0
4
0
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9.7% 10.5%
16.9%
20.1%
42.8%
 
Fig. 9 Ratio of variances of decomposed shoreline 
change 


Influence of long-period variation on shoreline change

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Influence of long-period variation on shoreline change

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