This paper investigates the following characteristics of run-up of random waves on gentle slopes experimentally: (1) the run-up wave energy spectrum, (2) the ratio of the number of run-up waves to that of incident waves, (3) the relationship between the representative run-up height, the deep-water wave steepness and the beach slope, (4) the run length of run-up heights, and (5) the effect of wave grouping on representative run-up heights. Main results are summarized in the chapter of conclusions.

The main purpose of this paper is to propose a model for prediction of the spatial distributions of representative wave heights and the frequency distributions of wave heights of irregular waves in shallow-water including the surf zone. In order to examine the validity of the model, some experiments of irregular wave transformation have been made. In addition, an attempt has been made to clarify the spatial distribution of wave grouping experimentally. Especially the present paper focuses finding the effects of the bottom slope and the deep-water wave steepness on the wave height distribution and wave grouping.

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