Velocity Probability Density Functions from Altimetry

Abstract

Probability density functions (pdfs) are employed to evaluate the distribution of velocities in the global ocean. This study computes pdfs of ocean surface velocity using altimetric data from the TOPEX/Poseidon satellite. Results show that the shape of the observed pdfs changes with the size of the domain over which they are calculated: if data are drawn from a small region of the ocean, the pdfs are Gaussian. As the area of the ocean considered increases, the pdfs take on more exponential shapes. The appearance of exponential pdfs is particularly pronounced when data are drawn from a large range of latitudes, while data drawn from constant latitude tend to have a more Gaussian pdf. The authors show that this distinction between zonal and meridional regions is also observed in acoustic Doppler current profiler measurements. The authors propose a simple statistical model to explain the observed velocity pdfs. This explanation depends on the fact that root-mean-squared velocity (or the width of velocity pdf) varies throughout the ocean. The velocity pdf is predicted from the distribution of the mean-squared velocity. The model matches the observations in predicting a pdf that is parabolic for small velocities with generalized exponential decay for large velocities.