**6. Reproduction of topographic changes relative to topography in 1947**

### **6.1 Calculation conditions**

The calculation domain is the same as that in the previous section. In the calculation, the entire period between 1947 and 2010 was separated into five periods, and *Q*in in each period was calculated from the volumetric change transformed from the shoreline changes measured during the period by multiplying the characteristic height of beach changes. In the first and second periods until 1962 and 1967, respectively, *<sup>Q</sup>*in was given as 6 <sup>10</sup><sup>4</sup> , and 4.7 <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> /year in the third, fourth, and fifth periods between 1967 and 2010 with a decrease in *Q*in by 20% after 1967.

For the initial topography, the results of the reproduction calculation until 1947 were employed, assuming parallel contour lines on the expanded coordinates. In the


**Table 2.** *Calculation conditions.* *A Long-Term Prediction of Beach Changes around River Delta using Contour-Line-Change Model DOI: http://dx.doi.org/10.5772/intechopen.85207*

calculation, the changes in contour lines between +3 and 8 m were calculated, assuming the same seabed slopes of 1/6 between *z* = +3 and 2 m, and 1/30 between *z* = 2 and 8 m. The number of grain sizes (*N*), the grain sizes of fine and coarse sand, the initial contents of each grain size of *μ*<sup>1</sup> and *μ*2, the equilibrium slope corresponding to each grain size, and the wave conditions are the same as those in the reproduction calculation. The longshore distribution of the initial breaker angle was given by subtracting the inclination angle of the shoreline reproduced in 1947 from the initial breaker angle in 1899. The change in wave field by the construction of structures was calculated using the angular spreading method for irregular waves. The wave transmission coefficient of detached breakwaters was set to *K*<sup>t</sup> = 0.2 as shown in **Table 2**, except for the detached breakwaters with *K*<sup>t</sup> = 0.4 placed between *x* = 1.4 and 0.5 km, and *K*<sup>t</sup> = 0.8 for artificial reefs.

#### **6.2 Results of the reproduction calculations**

#### *6.2.1 Change in contour lines*

overall shoreline changes were reproduced well, except for the river mouth area where the shoreline change was underestimated. Regarding the shoreline changes until 1967, the shoreline changes in the overall area including the shoreline recession west of the seawall constructed immediately west of the river mouth were well reproduced. The predicted and measured shoreline changes are in good agreement.

*Sedimentary Processes - Examples from Asia,Turkey and Nigeria*

**6. Reproduction of topographic changes relative to topography in 1947**

The calculation domain is the same as that in the previous section. In the calculation, the entire period between 1947 and 2010 was separated into five periods, and *Q*in in each period was calculated from the volumetric change transformed from the shoreline changes measured during the period by multiplying the characteristic height of beach changes. In the first and second periods until 1962 and 1967,

and fifth periods between 1967 and 2010 with a decrease in *Q*in by 20% after 1967. For the initial topography, the results of the reproduction calculation until 1947 were employed, assuming parallel contour lines on the expanded coordinates. In the

/year

/year,

/year,

/year, detached breakwater between *x* = 3.5 and 2.5 km,

/year,

/year, in which sand is subtracted at *x* = 13 km and nourished at *x* = 8 km,

artificial reef and detached breakwater between *x* = 5 and 0 km Incident wave angle Initial breaker angle in 1899 minus inclination angle of shoreline reproduced in

▪ Wave transmission coefficient *Kt* = 0.2 (detached breakwater) except *Kt* = 0.4

▪ Port breakwaters at Yodoe and Kaike fishing ports and Sakaiminato Marina

▪ Coefficient of Ozasa and Brampton's [18] term *<sup>ξ</sup>* = 1.62: detached breakwaters

Coefficient of Ozasa and Brampton's [18] term *ξ* = 3.24

Remarks ▪ Fluvial sand supply from Hino River: sand source distributed in depth zone

, and 4.7 <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup>

/year in the third, fourth,

/year was given by a sink and source of

**6.1 Calculation conditions**

respectively, *<sup>Q</sup>*in was given as 6 <sup>10</sup><sup>4</sup>

*<sup>Q</sup>*in 1 (1947–1962): 6 <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup>

1947

*Kt* = 0.0

Coefficient of sand transport

**Table 2.**

**78**

*Calculation conditions.*

2 (1962–1967): 6 104 <sup>m</sup><sup>3</sup>

4 (1980–1995): 4.7 104 <sup>m</sup><sup>3</sup>

and between 3.5 and 7 km, seawall between *x* = 5 and 0 km, and between *x* = 3.5 and 13 km 5 (1995–2010): 4.7 <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup>

sand back pass of 3 104 <sup>m</sup><sup>3</sup>

between *z* = +3 and 8 m

sand between *z* = 0 and + 3 m

between *x* = 1.4 and 0.5 km ▪ Artificial reef *Kt* = 0.8

between *x* = 1.4 and 0.5 km

detached breakwater Kaike fishing port,

seawall between *x* = 0 and 1.5 km 3 (1967–1980): 4.7 <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup>

and seawall between *x* = 0 and 3.5 km

L-shape groin between *x* = 7 and 8 km,

▪ Sand back pass by a rate of 3 <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup>

**Figure 15** shows the calculation results between the first and fifth periods together with an additional expression of bathymetric changes relative to the bathymetry in 1947 (**Figure A2**). In the first period (**Figure 15(a)**), erosion concentrated around the Hino River mouth with gradual accretion west of *x* = 4 km because of the decreased *<sup>Q</sup>*in of 6 <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> /year. Since the calculation was carried out using the expanded coordinates set on the shoreline in 1947, the triangular shoreline recession area shown in **Figure 15(a)** corresponds to the recession of the protruded shoreline of a river delta. The shoreline receded around the river mouth, whereas the contour lines advanced west of *x* = 5 km.

In the second period (**Figure 15(b)**), the seawall had been constructed between *<sup>x</sup>* = 0 and 1.5 km, although *<sup>Q</sup>*in was the same (6 <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> /year) as that in the first period. Owing to the construction of the seawall, westward longshore sand transport was partially blocked at the protruded seawall, resulting in erosion immediately west of the structure with the accretion upcoast. In the third period, *Q*in decreased from 6 104 to 4.7 <sup>10</sup><sup>4</sup> m3 /year together with the construction of 12 DBs and Kaike fishing port breakwaters (**Figure 15(c)**). Soon after the construction of DBs, cuspate forelands were formed behind the DBs. Simultaneously, severe erosion occurred downcoast of Kaike fishing port located at *x* = 3 km because of the decrease in the westward longshore sand transport.

In the fourth period, although *<sup>Q</sup>*in was the same (4.7 <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> /year) as that in the third period, new DBs were constructed between *x* = 3.5 and 2.5 km, and between 3.5 and 7 km, and further seawall was constructed between *x* = 5 and 0 km, and between *x* = 3.5 and 13 km, as shown in **Figure 15(d)**. At this stage, land reclamation was carried out at the west end at the shoreline, and the shoreline length was decreased by 4 km, resulting in the advance of all the contour lines. Although the shoreline east of the structures was stabilized by the construction of many coastal structures, erosion is severe downcoast.

In the fifth period between 1995 and 2010 (**Figure 15(e)**), *Q*in was kept constant at 4.7 <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> /year, the same as that in the fourth period. For the sand back pass, sand was excavated at a rate of 3 <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> /year at *x* = 13 km, and the same amount was supplied at *x* = 8 km. In addition to this, an L-shaped groin was constructed at *x* = 7 km, and an artificial reef and DBs were constructed between *x* = 5 and 0 km. The effect of blocking longshore sand transport by the land reclamation reached upcoast, and the contour lines between *x* = 13 and 7 km became straight.

*6.2.2 Depth changes*

*DOI: http://dx.doi.org/10.5772/intechopen.85207*

**Figure 16.**

**Figure 17.**

**81**

*Measured and predicted shoreline changes until 2007.*

*(b) Calculated (1967–2007).*

**Figure 16** shows the measured and predicted shoreline changes between 1967 and 2007. The shoreline advance behind the DBs, downcoast shoreline recession, and the shoreline advance upcoast of the west boundary were in good agreement in the measured and predicted results. **Figure 17** shows the entire shoreline changes

*A Long-Term Prediction of Beach Changes around River Delta using Contour-Line-Change Model*

*Measured and predicted shoreline changes between 1967 and 2007. (a) Measured (1967–2007).*

#### **Figure 15.**

*Bathymetric changes between first period (1947–1967) and fifth period (1995–2010). (a) First period (1947–1962). (b) Second period (1962–1967). (c) Third period (1967–1980). (d) Fourth period (1980–1995). (e) Fifth period (1995–2010).*

*A Long-Term Prediction of Beach Changes around River Delta using Contour-Line-Change Model DOI: http://dx.doi.org/10.5772/intechopen.85207*

#### *6.2.2 Depth changes*

**Figure 16** shows the measured and predicted shoreline changes between 1967 and 2007. The shoreline advance behind the DBs, downcoast shoreline recession, and the shoreline advance upcoast of the west boundary were in good agreement in the measured and predicted results. **Figure 17** shows the entire shoreline changes

#### **Figure 16.**

*Measured and predicted shoreline changes between 1967 and 2007. (a) Measured (1967–2007). (b) Calculated (1967–2007).*

**Figure 17.** *Measured and predicted shoreline changes until 2007.*

**Figure 15.**

**80**

*(1980–1995). (e) Fifth period (1995–2010).*

*Sedimentary Processes - Examples from Asia,Turkey and Nigeria*

*Bathymetric changes between first period (1947–1967) and fifth period (1995–2010). (a) First period (1947–1962). (b) Second period (1962–1967). (c) Third period (1967–1980). (d) Fourth period*

**A. Appendix**

*DOI: http://dx.doi.org/10.5772/intechopen.85207*

**Figure A1.**

**83**

*between 1920 and 1967.*

*Bathymetric changes until 1947, 1962, and 1967 with reference to bathymetry in 1920. (a) Bathymetric changes between 1920 and 1947. (b) Bathymetric changes between 1920 and 1962. (c) Bathymetric changes*

*A Long-Term Prediction of Beach Changes around River Delta using Contour-Line-Change Model*

**Figure 18.** *Distribution of longshore sand transport rate.*

until 2007 with reference to 1967. The predicted and measured shoreline changes agree well.

#### *6.2.3 Comparison between measured and calculated shoreline changes*

**Figure 18** shows the distribution of longshore sand transport in the entire study area. Between 1899 and 1929, sand supplied from the Hino River was transported to both directions away from the river mouth with the westward and eastward transport of 3.6 105 and 1.1 105 m3 /year out of the entire sand supply of 4.7 105 m3 /year, respectively. With the decrease in sand supply from the Hino River, the longshore sand transport had decreased from the vicinity of the river mouth. In particular, the westward longshore sand transport markedly decreased after the construction of the DBs between 1967 and 1973 in the area between *x* = 0 and 3 km. East of the river mouth, eastward longshore sand transport at the initial stage reversed until 1967, and westward longshore sand transport began to occur after 1967.

#### **7. Conclusions**

The topographic changes of the Yumigahama Peninsula between 1899 and 2010 have been reproduced using the contour-line-change model considering the change in grain size of the seabed material. It was found that the beach changes of this peninsula were involved in the process leading to the reduction in the size of the Hino River delta, and strong erosion occurred around the river mouth. Because countermeasures were carried out from up the coast, sand was deposited up the coast of various structures with erosion down the coast. It was concluded that the contour-line-change model considering the change in grain size of the seabed material is a useful tool for predicting long-term topographic changes.

*A Long-Term Prediction of Beach Changes around River Delta using Contour-Line-Change Model DOI: http://dx.doi.org/10.5772/intechopen.85207*
