Abstract. We quantify skill and uncertainty in observing the statistics of natural variability using observing system simulation experiments on an ensemble of climate simulations and an observing strategy of in situ measurements and objective mapping. The targeted statistic is the 0–700 m global ocean heat content anomaly as observed by the In Situ Analysis System 2013 (ISAS13) strategy of a long, equilibriated simulation of the Community Climate System Model (CCSM) version 3.5. Subannual variability is found to be significantly contaminated by the observing strategy, especially before 2005, primarily due to the sparseness and seasonality in the number and location of pre-Argo observations. However, one-year running means from 2005 onward are found to faithfully capture the natural variability of the model's true ocean heat content variability. During these years, synthetic observed annual running means are strongly correlated with the actual annual running means of the model, with a median correlation of 95 %, versus only 60 % for the observational record before 2005. When scaled to account for the fact that the real ocean is more variable than the model, root mean square errors in observing the annual-running mean natural variability of the global ocean heat content are estimated to be 6.2 ZJ for the pre-Argo era (1990–2005) and 2.1 ZJ for the Argo era (2005–2013) with relative signal-to-noise ratios of 1.9 and 14.7. Combining the estimated, scaled uncertainties of the observing strategy with its estimated trend, the 1990–2013 trend in global ocean heat content is found to be 5.3 ± 1.0 ZJ/yr.