Four years of the TOPEX/POSEIDON altimeter data are used to produce estimates of statistical space-time scales of ocean variabilities for the sea surface height. A three-dimensional (space-time) correlation function with an anisotropic directional dependence is assumed. The function has Gaussian distributions in radial directions in the space-time coordinates and ellipsoidal contour surfaces. The function can reveal the space-time scales and propagations of the variabilities and statistical errors in the altimeter data. We evaluated the space-time scales using the best fit correlation function to the altimeter data. The scales show geographical differences. This means that dominant variabilities depend on regions. We show an optimum interpolation (OI) method as an example of the application of the fitted correlation function. The OI is applied to the altimeter data in the space-time domain to make grid point data with higher accuracy than those obtained from a usual spatial (two-dimensional) OI (2-D OI). The values of the correlation function are used for the correlation coefficients of the first guess error in the OI. A propagation diagram obtained from the space-time OI (3-D OI) shows clear propagations of planetary disturbances with larger amplitude. The grid point values from the 3-D OI show better correspondences with sea levels from tide gauges than those from the 2-D OI. The advantage is due to the data of the different cycles being additionally adopted and the correlation function reflecting propagation of the ocean variabilities. ¿ 2000 American Geophysical Union