1217

DYNAMIC TOPOGRAPHY CHANGES OF SAND SPIT OF THE
TENRYU RIVER MOUTH DUE TO OVERTOPPING WAVESTOMOHIRO TAKAGAWA1, YOSHIMITSU TAJIMA1 HAIJIANG LIU1, SATOSHI
TAKEWAKA2, SHINJI SATO1
1.
2.

Department of Civil Engineering, The University of Tokyo, Hongo 7-3-1, Bunkyoku, Tokyo, 113-8656 Japan. takagawa@coastal.t.u-tokyo.ac.jp.
Department of Systems and Information Engineering, The University of Tsukuba,
Tennodai 1-1-1, Tsukuba, Ibaraki, 305-8573 Japan. takewaka@kz.tsukuba.ac.jp.
Abstract: In October 2009, the category-5 typhoon T0918 hit the Japan Pacific
Coast and significant topographic changes occurred along the Enshu-nada coast due
to the storm waves. The significant wave height was more than 10 m and rapid
landward migration of the sand spit of the Tenryu river mouth was observed. Basedon X-band radar image analysis, spatial and temporal changes of overtopping waves
and corresponding sediment flux across the sand spit were revealed. Spatialconcentration of the sediment flux can be explained by the nonlinear relationshipbetween wave height of overtopping waves and corresponding sediment fluxes. A
sediment flux model was developed based on the relationship. Maximum flux wasestimated by the model to be 51 m3/m/hour, which was achieved when high waves
and high tide were observed simultaneously.

Introduction
Coastal topography changes rapidly due to storm waves. In October 2009, thecategory-5 Typhoon T0918 (Melor) hit the Japan Pacific Coast (Fig. 1). The
central atmospheric pressure of the typhoon reached 910 hPa and maximum
wind speed recorded 55 m/s. The Tenryu River mouth area, shown in Figure 1, isone of areas that suffered the most significant topographic changes due toT0918. The significant wave height marked more than 10 m (Fig. 2). The sandspit at the mouth of the Tenryu River migrated landward about 50 m (Fig. 3).
From the viewpoint of coastal sediment management, it is very important toreveal the sediment movement and corresponding topographic change around thesand spits of river mouths, because the sand spit morphology affects both flow
and wave fields and sediment movements (e.g. Tajima et al. 2011). However,observationally-based analysis of sediment movement is limited in such extreme
wave event because of the difficulty of installation of observation equipments
under high-energy conditions. In this study, a remote sensing technology of Xband radar was utilized for wave observation. Overtopping waves across thesand spit were successfully captured in the X-band radar observation. This study
aims to establish a sediment transport model on overtopping waves across sand

1218

spits or bars through the analysis of overtopping waves and topographic changes
during the T0918 event.

Fig. 1. The path of typhoon T0918 and the location of study area. The typhoon’s positions every 3
hours are shown as circles. The gray scale indicates the central pressure of the typhoon.

Fig. 2. Temporal changes of discharge of the Tenryu River, significant wave height, wave period andmean water level.

1219

Fig. 3. Topographies around the Tenryu river mouth in August and October 2009. The arrows near thepoint P in the lower figure indicate the fallen directions of reed grasses shown in Fig. 4.

Topography Changes during T0918
Two topography data sets around the Tenryu River mouth were analyzed, one
was measured in August, before the typhoon, and the other in October, just after
the typhoon (Fig. 3). These data sets were obtained by the Ministry of Land,
Infrastructure and Transport (MLIT), Japanese Government. Between Augustand October, no flood and high wave events happened except the T0918 event.
Therefore, most of topographic changes between those data sets are thought tobe caused by high waves generated by T0918. In the focusing area of 2.5×106 m2
around the sand spit as shown in Figure 4, total budget of sediment volumetricchange including void was 3.0×103 m3. Sea-side of the spit was severely eroded,
while the land-side of the spit and offshore of the eroded areas wereaccumulated. As a result of these sedimentation and erosion, the spit migrated
about 50 m landward. No significant topographic changes were observed both in

1220

the river area near the north end of the analyzed area and also in the offshore
area deeper than −6 m T.P. Therefore, the sediment flux across the boundaries offocusing area is negligible. To capture the sediment movement over the spit,
total increases of sediment volume along the landward part were calculated ineach north-south section with 5 m intervals (Fig. 5). The boundary between
landward and seaward parts is shown as the S−S’ line in Figure 4. This boundary
was set along the crest of sand spit in August 2009. Assuming zero sediment
flux across the boundaries of the focusing area, sediment volume corresponding
to the landward sand flux across the sand spit was obtained in each section. Totalsediment volumes moved landward across the spit was estimated as 8.2×104 m3.
Alongshore distribution of landward sediment flux shows local concentration in
the middle and east end of the spit (B and D sections in Fig. 5), where the crest
height of the sand spit was lower than the other areas. This indicates that thesediment movement is strongly affected by the sand spit topography.

Fig. 4. Topography changes between August and October 2009. The arrows indicates estimatedsediment fluxes across the crest of the sand spit.

Fig. 5. The elevation change of the crest of sand spit between August and October 2009. The solid line
indicates estimated sediment fluxes across the crest of the sand spit.

1221

Overtopping Waves during T0918
Field survey was conducted just after the typhoon in order to capture theevidence of overtopped waves. Most of reed grasses fell down in landward
direction in the north-west area of the sand spit (Fig. 6). This area was more than
200 m away from the shoreline, where moderate waves could not reach. The
direction of reeds indicates the running direction of overtopping waves as shownin Fiture 3. Fan shaped over-wash sand sheet deposits were observed in west end
and middle area (Fig. 4).
A X-band radar survey was also conducted during the storm event. The radarsystem has been installed on the rooftop of a building located at the right-side of
the Tenryu River mouth (Fig. 3). The observation area is 5.3 km × 5.3 km. Radarecho signals were processed and recorded as an 8-bit gray image of 1024×1024
pixels (Fig. 7). It is known empirically that wave crests were shown as highbrightness lines in those images (Hasan & Takewaka, 2009). Image data wereobtained every 2 seconds. The propagation of waves is observed from asequence of radar images. Cross-shore time stack images were used to detect theovertopping waves. A typical time stack image is shown in Figure 7. The image
shows temporal changes of a north-south section of radar images. Bright pixels
moving northward with time indicates the motion of wave crests. In this figure,some wave crests stop in the sand spit area, while the others shown as arrows
keep moving all over the area and reach the riverside of the spit. The later case isthought as an overtopping wave. In this way, overtopping waves were detected

Fig. 6. Reed grasses fell down in the north direction at the point of P in Fig.3. The broken line shows afront of sand-sheet deposits.

1222

Fig. 7. X-band radar image (left) and cross-shore time stack image (right). Arrows show overtopping
waves across the sand spit.

and counted manually by eyes in each north-south section with 50 m-intervals.
Temporal and spatial changes of overtopping wave ratio were shown in Figure 8.
The overtopping wave ratio Pe is defined as
Pe = N e N(1)

where Ne is number of overtopping waves in a unit of time and N is number ofincident waves in a unit of time. Ne was obtained by X-band radar analysis and N
was calculated by the wave period data recorded at the Ryuyo wave gauge, about
1000m offshore from the river mouth with water depth of 40m.

Fig. 8. Temporal and spatial changes of ratio of overtopping waves and over-wash sand flux estimatedby the proposed model.

1223

Fig. 9. Schematic diagram of model parameters.

Estimation of run-up heights
Parameters characterizing run-up and overtopping waves are shown in Figure 9.
In order to simplify the treatment of wave height, hypothetical slope continuing
upward beyond the crest of sand spit was assumed. Both of run-up andovertopping wave height were defined as the hypothetical run-up height on thehypothetical slope.
Based on field survey and laboratory observation on monochromatic waves(Hunt, 1959; Holman, 1986), wave run-up height R is typically parameterized as
R H 0 = cξ + d(2)where H0 is the offshore wave height and c and d are dimensionless constants.
ξ is a non-dimensional “surf similarity parameter” used in characterizing surfzone processes (Iribarren and Nogales, 1949) and is given byξ = tan β

H 0 L0(3)where tan β is the beach slope, L0 is the deep water wave length defined as L0 =gTs2/2π by linear theory, g is the gravity acceleration, and Ts is the significant
wave period.
Assuming that the probability density distribution of incident wave height
follows Rayleigh distribution and surf similarity parameter does not vary with1224

individual wave properties, the probability density distribution of run-up heightalso follows Rayleigh distribution and is given as
P (R ) =( π  R 2 
−   exp
 4R 2 R24π R)

where R is the average of R. Then the probability Pe of R exceeding Rcr is givenby π  R 2 ∞
Pe = ∫ P (R )dR = exp −  cr  Rcr
 4 R  
(5)where Rcr is the critical run-up height for over-wash event. Rcr is given by Rcr =hc − η , where hc is the height of the sand spit crest and η is the mean waterlevel. Here the average height of sand spit crests on August and October 2009 ineach alongshore point was used as hc. η was obtained from Ryuyo wave gauge
data.
Empirical parameters c and d can be determined by using the least square
method to minimize the difference between the Pe obtained by using Eq. 1 andthe Pe calculated by using Eqs. 2, 3, and 5. Once these parameters weredetermined, R can be evaluated only from wave gauge data and topography
data of sand spit. However, large value of Pe is problematic because R willreach an infinite value when Pe comes close to 1. In this procedure, it is difficult
to estimate reliable value of R when Pe is close to 1. Furthermore, it is alsodifficult to count overtopping waves in X-band time stack images when Pe ismore than 0.5. In such case, overlaps of waves happen frequently and it is hardto distinguish individual incident waves in surf zone. Therefore, R was decided
to estimate by empirical extrapolation on the basis of the relationshipbetween R and H0 when Pe is more than 0.5. The relationship is shown in Figure
10. The data was selected in the smaller Pe case. Finally, an empirical
relationship was obtained by the least square method as follows:
R = 0 .101 H 0 + 0 .514

(6)

where the unit of R and H0 is in meter. This empirical formula was used toestimate R when Pe is more than 0.5. This estimation was applied for only 7 %of all data in this study.

1225

Fig. 10. Relationship between H0 and R . A-D indicate the data from A-D section of Figure 3.

Sediment transport model on overtopping waves
Sediment flux q is usually modeled in the power model as a product of flow
velocity and bottom shear stress. Bottom shear stress for rough turbulent flow is
proportional to the square of flow velocity. The flow velocity at the crest of sandspit is thought to be proportional to the square root of excess run-up height Re =R – Rcr because the run-up wave motion on an uniform slope is wellapproximated by parabolic motion (e.g. Shen & Meyer, 1963; Roberts et al,2010). Therefore, the following relation is assumed.
3(7)q ∝ Re 2

Therefore, sediment flux was modeled asq ∝ κReγ(8)where κ and γ are regression coefficients. γ was expected close to 1.5. According
to Eq. 8, the total landward over-wash sediment flux at each point of sand spit
crest during the typhoon event is given by∞

Qmodel = ∫ ∫ κRe ⋅ P(Rcr + Re ) ⋅ NdRe dtγ(9)0The regression coefficients were estimated by the least square method so that thedifference between the total sediment flux Qmeasurement obtained by the1226

topographic analysis and the total sediment flux Qmodel evaluated by the proposedmodel. The estimated value of κ and γ are 0.0911 and 1.71, correspondingly. Thevalue of γ is near to the expected value of 1.5. The relationship Qmeasurement andQmodel is shown in Figure 11. They are well correspondent with each other.
Figure 8 shows temporal and spatial changes of over-wash sediment flux
estimated by the proposed model. As shown in Figure 8, Sediment flux
distribution was more concentrated both spatially and temporally than the ratioof overtopping waves. According to the model, maximum flux was estimated tobe about 51 m3/m/hour. Over 70 % of total volume of sand transportation during
the typhoon was transported within 4 hours around 5 a.m. on October 8 whenhigh waves and high tide were observed simultaneously. Therefore, over-washedsediment motion generated by overtopping waves across a sand spit is found tobe highly concentrated phenomena both temporally and spatially.

Fig. 11. Comparison between the sediment flux Qmeasurement and Qmodel.

Horizontal distribution of wave fieldOn the analysis above, alongshore variation of wave field was neglected tosimplify the phenomena. To capture the alongshore variability, Figure 10 wasexamined again here. In this figure, R of sections B and D shows larger value
than A and C. This implies that other factors neglected in the proposed model
still affect the run-up heights. Alongshore variation of wave field is thought to be
one of those factors because R is related with alongshore location.
To examine alongshore variation of wave field, a sequence of X-band radar
images at 5 a.m. on Oct. 8 was analyzed by using Particle Image Velocimetry

1227(PIV) technique. Horizontal wave celerity field obtained by PIV is shown in
Figure 12. Arrows show local concentration of waves around sections B and D.
These local concentrations are thought to be caused by wave refraction which isrelated to topography and wave-current interaction. These alongshore effects
should be counted in sediment transport analysis to improve the model.

Fig. 12. Wave celerity distribution on October 8 at 5:00 a.m.

Conclusions
Local concentration of sediment transport across the sand spit was observed in afield survey and topography data analysis. Based on X-band radar image
analysis, spatial and temporal changes of overtopping waves and corresponding
sediment flux across the sand spit were revealed. Sediment flux distribution wasmore concentrated both spatially and temporally than the ratio of overtopping
waves. A sediment transport model on overtopping waves across sand spits wasestablished in this study. The model parameters are empirically estimated on thebasis of observation data analysis. According to the model, maximum flux wasestimated to be about 51 m3/m/hour. Over 70 % of total volume of sandtransportation during the typhoon was transported within 4 hours around 5 a.m.
on October 8 when high waves and high tide were observed simultaneously.

Acknowledgements
This study is a part of Tenryu-Enshunada Project, “Dynamic sedimentmanagement and coastal disaster prevention by advanced technologies”
supported by the Special Coordination Funds for promoting Science andTechnology of Ministry of Education, Culture, Sports, Science and Technology,
Japan. Authors would like to appreciate to Ministry of Land, Infrastructure,
Transport and Tourism for wave and topography data.

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