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The purpose of this paper is to propose the quasi-linear theory of tsunami run-up and run-down on a beach with complex bottom topography. We begin with the one-dimensional nonlinear shallow-water wave equations, which we consider over a beach of complex geometry that can be modeled by a piecewise continuous function, along with several natural initial and boundary conditions. The primary obstacle in solving this problem is the moving boundary associated with the shoreline motion. To avoid this difficulty, we replace the moving boundary with a stationary boundary by applying a transformation to the spatial variable of the computational domain. A characteristic feature of any tsunami problem is the smallness of the parameter ε=η0/h0, where η0 is the characteristic amplitude of the wave, and h0 is the characteristic depth of the ocean. The presence of this small parameter enables us to effectively linearize the problem by using the method of perturbations, which leads to an analytical solution via an integral transformation. This analytical solution assumes that there is no wave breaking. In light of this assumption, we introduce the wave no-breaking criterion and determine bounds for the applicability of our theory. The proposed model can be readily used to investigate the tsunami run-up and draw-down for different sea bottom profiles. The novel particular solution, when the seafloor is described by the piecewise linear function, is obtained, and the effects of the different beach profiles and initial wave locations are considered.

In this research, land cover changes in the coastal region of Turkey were analyzed using the Corine dataset between 1990 and 2018. Changes in each period were analyzed by using the rate of change and the annual rate of change, the transition matrix of net changes, and the transition probability matrix. In order to predict land cover change trends and to determine future land cover change probabilities, a combination of Markov and cellular automata models was used. It was determined that the highest increase in each study period was in artificial surfaces and the highest decrease was in the forest and the semi-natural area. The total forest areas were converted to the other land cover type in the first study period amounting to 2479.32 km 2 . Also, it was decreased and transformed by about 62.47 km 2 , 118.82 km 2 , and 203.09 km 2 of the forest area that existed in the second, third, and fourth periods respectively. The results indicate that the probabilities of the increasing area will be covered by artificial surfaces and agricultural areas. It is estimated that the rate of 57% in 1990, the initial year of the forest areas, will decrease to 53.4% in 2034 and to 53% in 2050. Also, the rate of 2.1% in 1990, the initial year of the artificial surfaces, will increase to 4.5% in 2034 and to 5.0% in 2050. It is seen that more artificial surfaces will be needed in the Turkish coastal region due to the increasing population and number of tourists. It is important to evaluate and investigate the coastal areas where more artificial areas are expected to be needed within the scope of the coastal area management plans to be prepared at the national scale., (© 2022. The Author(s), under exclusive licence to Springer Nature Switzerland AG.)