Good agreement is found between global patterns of TOPEX dynamic height and expendable bathythermograph (XBT) heat storage anomalies from approximately 30 ¿S to 60 ¿N for the 2-year period from 1993 to 1994, with both variables dominated by the biennial signal. This is due to the physical dependence of absolute dynamic height upon relative steric height (i.e., an alias of heat storage). Regression finds these two variables correlated from 0.5 to 0.8 over the global ocean, with slopes of regression ranging from 0.05 to 0.15¿109 W-s m-2 cm-1. While these statistics are not definitive, they do provide representative estimates of regression error, sampling error, and sampling frequencies for determining the role that TOPEX altimetry can play in estimating upper ocean heat storage over large portions of the global ocean. We examine this role within the framework of optimum interpolation methodology (Gandin, 1963), finding regression errors for inferred heat storage anomalies larger than instrumental errors expected from XBT heat storage estimates but of the same order as uncertainties incurred from subgrid ambient noise. While this increases the noise-to-signal ratio of the inferred heat storage anomalies by a factor of 2, the greater density of TOPEX observations reduces the interpolation errors for gridded fields of upper ocean heat storage anomalies to half those incurred from the smaller density of XBT sampling. So, when inferred heat storage anomalies are used to compute the time sequence in upper ocean heat storage anomaly over large portions of the global ocean during 1993--1994, errors of ¿2 W m-2 are half those achieved with XBT sampling. Moreover, the time rate of change in upper ocean heat storage anomalies becomes statistically significant, with inferred heat storage anomalies in the North Atlantic Ocean remaining constant for 1993--1994 but increasing in both the Indian and Pacific Oceans. The latter dominate the time rate of change of upper ocean heat storage anomaly over the global ocean, yielding an average rate of 3 W m-2 over the 2-year period. ¿ American Geophysical Union 1995