Spatial Point Process Model Of Wave Breaking

Wind wave breaking in deep water plays an important role in the process of theair-sea interaction. It is the main source of ocean surface turbulent and the mainmechanism of limit of wave height and maintenance of wave energy dissipation of thewave field. However there is an essential problem through the study of wave breaking,which is the spatial point pattern. If we can establish the spatial point model aboutbreaking waves, we will treat the breaking waves in a more comprehensive way.The white-cap is the the major form of the waves breaking, and is also theimportant aspect that people are familiar with waves breaking and do research about it.For a long time, the research on it mainly focus on two aspects:(1)the probabilitywhite-cap cover, and the relationship between it and the wind speed, atmosphericstability, water temperature and other factors;(2)the average length of thebreaking-wave crest line Λ(c)in the range of (c,c+dc). All of the study thar weshowed above did not concern of the research about the spatial point pattern ofbreaking waves. However the spatial pattern analysis of white-cap is just theprecondition of breaking statistical research. If we make the gravity of the breakingwhite-cap as a point in R~2, all the gravities in the given area at any moment form aspatial point process. Under the theory of the spatial point process, the characteristicsstudied before can be treated as the mark of the process. Consequently, we can use thespatial marked point processes to describe the probability of the white-cap breaking.Obviously we can have a more in-depth understanding and discussion about therandomness and the dissipation of the breaking waves.Based on spatial point process theory, we introduce it into the breaking study,and come up with using the statistical inference tools of spatial point process to studythe spatial distribution model of white-cap breaking. Combined with the practicalbreaking white-cap images, we calculate the L-function and the K-function of the observed patterns, and use MCMC random simulation test against the null hypothesisabout homogeneous Poisson process, making the K-function as the basic statistics forinferring that the spatial point pattern of the observed images we chose ishomogeneous Poisson process. However, the result of goodness-of-fit test shows thatwe should refuse the null hypothesis. Then we choose the inhomogeneous Poissonmodel as the null hypothesis to make new MCMC test. The graphics show that thenew null hypothesis are more correctly.Although we have many work to do for modeling the spatial point process modelof wave breaking, we can consider that the spatial model of breaking have clustercharacteristic. The case studies show that the statistical tools of spatial point processcan be effectively used for the research of white-cap breaking.