Estimating sampling uncertainty in fixed-depth and fixed-isotherm estimates of ocean warming

We present a simple, generic method for parameterising the sampling and measurement uncertainty for time series data that is based on the number of observations that constitutes each data point. The method is demonstrated using basin-averaged monthly time series of (1) the mean temperature above 220 m depth (T_220m); (2) the mean temperature above the 14 °C isotherm (T_14C) and (3) the depth of the 14 °C isotherm (D_14C). The T_220m and T_14C analyses are in some sense 'equivalent', since the spatial-time-mean depth of the 14 °C isotherm is approximately 220 m. In agreement with oceanographic theory, we find that the T_14C time series has a consistently lower associated sampling uncertainty than T_220m for all ocean basins considered in this study. We also note that the sampling uncertainty for all quantities for a given number of observations is dependent on ocean basin. Our results suggest that with the current observing array we are able to monitor global monthly values of T_220m, T_14C and D_14C with a measurement and sampling uncertainty of approximately ± 0.07 °C, ± 0.04 °C and ± 2.4 m, respectively. However, these estimated uncertainties will become much larger on moving to regional or smaller scales.