Understanding the ocean requires determining and explaining global integrals and equivalent average values of temperature (heat), salinity (freshwater and salt content), sea level, energy, and other properties. Attempts to determine means, integrals, and climatologies have been hindered by thinly and poorly distributed historical observations in a system in which both signals and background noise are spatially very inhomogeneous, leading to potentially large temporal bias errors that must be corrected at the 1% level or better. With the exception of the upper ocean in the current altimetric-Argo era, no clear documentation exists on the best methods for estimating means and their changes for quantities such as heat and freshwater at the levels required for anthropogenic signals. Underestimates of trends are as likely as overestimates; for example, recent inferences that multidecadal oceanic heat uptake has been greatly underestimated are plausible. For new or augmented observing systems, calculating the accuracies and precisions of global, multidecadal sampling densities for the full water column is necessary to avoid the irrecoverable loss of scientifically essential information.


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