**2.2. Lakeshore in Lake Saroma**

**Figure 4** shows a satellite image of an abandoned inlet located at the east end of Lake Saroma in Hokkaido, Japan (Location: 44°08′03"N, 143°59′04″E) [10]. This water body has a triangular shape, and segmentation of a water body can be seen near the east end. When enlarging the rectangular area in the satellite image of **Figures 4** and **5** is obtained. For the wind rose in Lake Saroma, the predominant wind direction is WNW, resulting in the eastward development of sand spits. On the south shore is Tofutsu fishing port, as shown in **Figure 5**. East of

**Figure 3.** Segmentation and development of sand spits along lakeshore of Lagoa de Mangueira in Brazil [7].

**Figure 4.** Study area in eastern Lake Saroma [10].

this fishing port, the width of the water body gradually decreases, and sand spits A-E develop together with pairs of sand spits A' and E'. Of these sand spits, sand spits A and A' are the largest and divide the water body into two. In the vicinity of sand spit A', wind waves cannot be generated in the presence of the westerly wind, resulting in no development of sand spits. However, east of sand spit A', wind waves can develop, and the size of the sand spits increases eastward in the order of sand spits B, C, and D.

Kitaura is N18°W, the predominant wind of NNE blows at an angle of 40.5° clockwise relative to the direction of the principal axis. Because of this oblique wind direction, wind waves are incident at a large incidence angle to the shoreline, resulting in the formation of the protruding shoreline on the west shore. In particular, an enlarged satellite image of two subareas, **a** and **b**, in **Figure 6** is shown in **Figure 7**. In subarea **a**, cuspate forelands and the ridges develop out of phase, and this condition is very similar to that in the lagoon facing the Chukchi Sea, as shown in **Figure 2**. Similarly, the cuspate forelands on both shores extend out of phase in subarea **b**. This shows a typical example of segmentation and the development of sand spits

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**Figure 6.** Cuspate forelands developed along lakeshore of Lake Kitaura in Japan [5].

**Figure 7.** Enlarged satellite images of areas a and b in Lake Kitaura [5].

in a triangular lake.

## **2.3. Lakeshore in Lake Kitaura**

Lake Kitaura located in Ibaraki Prefecture is a shallow lake with an area of 35.2 km2 and 25 km length in the north-south direction, as shown in **Figure 6**. The formation of cuspate forelands in this lake was discussed in [5], and here we refer this results. This lake is located in the lowland surrounded by Kashima and Namegata tablelands with elevations of 40 and 30 m on the east and west sides, respectively. Thus, wind waves can be generated without a significant sheltering effect by hills or mountains. Because the direction of the principal axis of Lake

**Figure 5.** Enlarged satellite image of rectangular area in **Figure 4**, and sand spits A-E and E' [10].

Segmentation of Water Body and Lakeshore Changes behind an Island Owing to Wind Waves http://dx.doi.org/10.5772/intechopen.72550 53

**Figure 6.** Cuspate forelands developed along lakeshore of Lake Kitaura in Japan [5].

Kitaura is N18°W, the predominant wind of NNE blows at an angle of 40.5° clockwise relative to the direction of the principal axis. Because of this oblique wind direction, wind waves are incident at a large incidence angle to the shoreline, resulting in the formation of the protruding shoreline on the west shore. In particular, an enlarged satellite image of two subareas, **a** and **b**, in **Figure 6** is shown in **Figure 7**. In subarea **a**, cuspate forelands and the ridges develop out of phase, and this condition is very similar to that in the lagoon facing the Chukchi Sea, as shown in **Figure 2**. Similarly, the cuspate forelands on both shores extend out of phase in subarea **b**. This shows a typical example of segmentation and the development of sand spits in a triangular lake.

**Figure 7.** Enlarged satellite images of areas a and b in Lake Kitaura [5].

**Figure 5.** Enlarged satellite image of rectangular area in **Figure 4**, and sand spits A-E and E' [10].

this fishing port, the width of the water body gradually decreases, and sand spits A-E develop together with pairs of sand spits A' and E'. Of these sand spits, sand spits A and A' are the largest and divide the water body into two. In the vicinity of sand spit A', wind waves cannot be generated in the presence of the westerly wind, resulting in no development of sand spits. However, east of sand spit A', wind waves can develop, and the size of the sand spits

length in the north-south direction, as shown in **Figure 6**. The formation of cuspate forelands in this lake was discussed in [5], and here we refer this results. This lake is located in the lowland surrounded by Kashima and Namegata tablelands with elevations of 40 and 30 m on the east and west sides, respectively. Thus, wind waves can be generated without a significant sheltering effect by hills or mountains. Because the direction of the principal axis of Lake

and 25 km

Lake Kitaura located in Ibaraki Prefecture is a shallow lake with an area of 35.2 km2

increases eastward in the order of sand spits B, C, and D.

**2.3. Lakeshore in Lake Kitaura**

**Figure 4.** Study area in eastern Lake Saroma [10].

52 Applications in Water Systems Management and Modeling

**3. Model for predicting lakeshore changes**

*H*1/3 was calculated using Wilson's formula [11, 12].

F(*i*+1) = *F*(*i*)

domain ABCD and another coordinate system (*xw*, *yw*) [13].

number along the *xw*-axis.

*H*1/3 = *f*(*F*, *U*) = 0.30{1 − [1 + 0.004 (*gF*/*U*<sup>2</sup>

For the calculation of the segmentation of a rectangular water body, the BG model employed for the calculation of oriented lakes [8] was used. Given a local fetch distance *F* at a given point (*g* is the acceleration due to gravity and *U* is the wind velocity), the significant wave height

Segmentation of Water Body and Lakeshore Changes behind an Island Owing to Wind Waves

In this calculation, a coordinate system (*xw*, *yw*) was set corresponding to the wave direction instead of a fixed coordinate system (*x*, *y*) for the calculation of beach changes with the rectangular calculation domain, ABCD, as shown in **Figure 10**, and the wave height was calculated in the rectangular domain A'B'C'D' including the domain ABCD. Neglecting the wave refraction effect, waves were assumed to propagate in the same direction as the wind. The fetch distance *F* was added from upwind to downwind along the *xw*-axis using Eq. (2) when the *xw*-axis was divided by mesh intervals Δ*x*w [13]. Here, the index *i* in Eq. (2a) is the mesh

r = {

1 (*Z* ≤ 0)

**Figure 10.** Selection of coordinate system (*x*, *y*) adopted for calculation of beach changes with rectangular calculation

)1/2 ] -2

+ r∆*xw* (2a)

0 (*<sup>Z</sup>* <sup>&</sup>gt; 0) (2b)

}(*U*<sup>2</sup> /*g*) (1)

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**Figure 8.** Satellite image of Lake Balkhash in Kazakhstan.

**Figure 9.** Enlarged satellite image of Lake Balkhash.

#### **2.4. Lake Balkhash**

Lake Balkhash has 450 and 200 km lengths in the E-W and S-N directions, respectively (**Figure 8**). **Figure 9** shows an enlarged satellite image of the rectangular area in **Figure 8**. Island A is located at a location of 46°34′53.99"N and 78°50′17.47″E at the central part of the lake near the east end, and a cuspate foreland of 14 km length extends between island A and the lakeshore. On the shore opposite to island A, a triangular cuspate foreland B is formed with a barrier island. The sand bar extending northwestward from Island A is symmetric with respect to the centerline of the cuspate foreland, and the length of the sand bar is longer than the width of the island. From this, it is inferred that the cuspate foreland extended from the land to Island A by the sand supply from Island A and the land, and connected to Island A.
