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The BG model (a model for predicting 3D beach changes based on the Bagnold’s concept) was introduced, and the fundamental aspects of the model were explained. The BG model is based on the concepts such as (1) the contour line becomes orthogonal to the wave direction at any point at the final stage, (2) similarly, the local beach slope coincides with the equilibrium slope at any point, and (3) a restoring force is generated in response to the deviation from the statically stable condition, and sand transport occurs owing to this restoring force. The same concept has been employed in the contour-line-change model and N-line model. In these studies, the movement of certain contour lines was traced, but in the BG model, 3D beach changes were directly calculated.

The segmentation and merging of elongated shallow water body with a large aspect ratio by wind waves were predicted using the Type 6 BG model. The deformation of a circular lake by wind waves was also studied when a straight seawall cutting a part of the water body was constructed in a lake for land reclamation, together with the investigation on the effect of the construction of detached breakwaters to the surrounding lakeshore. Finally, the formation of oriented lakes, groups of lake basins with a common long-axis orientation found in vast areas of the Arctic Coastal Plain, was predicted using the Type 6 BG model.

Beach changes related to human activities, such as the effect of construction of groynes and detached breakwaters on a coast with prevailing longshore sand transport, and offshore sand mining, which have engineering importance, were predicted using the Types 1 and 2 BG model. When a long port breakwater is extended, a large wave-shelter zone is formed and dominant longshore sand transport is induced from outside to inside the wave-shelter zone, resulting erosion outside the wave-shelter zone and accretion inside the wave-shelter zone. These beach changes were also predicted using the Type 2 BG model with the evaluation of the effect of a jetty extended at the port entrance to reduce sand deposition inside the port.

Eight types of the BG models are introduced in this chapter. The Type 1 is a model using wave parameters at the breaking point. In the Type 2, the effect of longshore sand transport due to the effect of the longshore gradient of breaker height is included with an additional term given by Ozasa and Brampton. In the Type 3, the intensity of sand transport P is assumed to be proportional to the third power of the amplitude of the bottom oscillatory velocity um due to waves, and in the Type 4, P is given by the wave energy dissipation rate due to wave breaking at a local point. In the Type 5, wave power is calculated using the coordinate system different from that for the calculation of beach changes to predict the topographic changes of an island or a cuspate foreland in a shallow water body under the action of waves randomly incident from every direction. In the Type 6, the height of wind waves is predicted using Wilson’s formula using the wind fetch distance and wind velocity, and then sand transport fluxes are calculated. The Type 7 is a model for predicting the formation of the ebb-tidal delta under the combined effect of waves and ebb-tidal currents with an analogy of the velocity distribution of ebb-tidal currents to the wave diffraction coefficient, which can be calculated by the angular spreading method for irregular waves. In the Type 8, the effect of the nearshore currents induced by forced wave breaking is incorporated into the model by calculating the nearshore currents, taking both the wave field and the current velocity at a local point into account.

The formation of land-tied islands as a result of the extension of a cuspate foreland, when waves were incident to several islands composed of sand from two opposite directions, was first investigated, taking a land-tied island offshore of Shodoshima Island in the Seto Inland Sea, Japan, as an example, and their topographic changes were predicted using the Type 5 BG model. Then, the interaction among multiple circular sandy islands on flat shallow seabed owing to waves was investigated, taking the islands in Hingham Bay near Boston Harbor as an example. On the basis of this example, topographic changes were also predicted using the Type 5 BG model.

The formation of a cuspate foreland when waves were incident from two opposite directions was investigated, taking a cuspate foreland extending at the northeast end of Graham Island in British Colombia of Canada and the cuspate forelands formed at the tip of Hon Bip Island north of Nha Trang, Vietnam, as the examples. The formation of such a cuspate foreland was predicted using the Type 4 BG model. Then, the development of multiple sand spits with rhythmic shapes in a shallow water body was investigated, taking the Sea of Azov in Russia as the example. Furthermore, the development of sand spits and cuspate forelands with rhythmic shapes was predicted, assuming that the waves were obliquely incident at angles of 60° relative to the direction normal to the shoreline or at angles of ±60° with probability p1:p2 = 0.50:0.50, 0.60:0.40, 0.65:0.35, 0.70:0.30, 0.75:0.25, and 0.80:0.20.

Beach changes on a coast subject to waves and seaward or shoreward strong currents were predicted using the Type 7 and 8 BG models. The formation of an ebb tidal delta subject to strong ebb tidal currents was studied first, taking the Imagire-guchi inlet connecting Lake Hamana with the Pacific Ocean as an example, and the long-term evolution of the tidal inlet was investigated using the bathymetric survey data. Then, the formation of a dynamically stable ebb tidal delta was predicted. Regarding the beach changes on a coast subject to waves and shoreward strong currents, the Type 8 was applied to the Kaike coast, where an artificial reef was constructed in place of a detached breakwater, resulting in the occurrence of strong shoreward currents over the artificial reef. A stable cuspate foreland behind a detached breakwater disappeared after the conversion of a detached breakwater into an artificial reef, suggesting that the artificial reef was less effective in sand deposition effect than the detached breakwater. Such beach changes were numerically predicted.

The formation of a sand spit and bay barrier was predicted using the BG model, covering three topics: (1) formation of a bay barrier in flat shallow sea and merging of bay mouth sand spits (Section 2), (2) elongation of a sand spit on a seabed with different water depths (Section 3), and (3) deformation of a sandbar formed at the tip of the Futtsu cuspate foreland owing to a tsunami which propagated into Tokyo Bay after the Great East Japan Earthquake on March 11, 2011 (Section 4). The Type 5 BG model was employed in Section 2, and Type 3 BG model in Sections 3 and 4.