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We construct a novel framework to investigate the uncertainties and biases associated with estimates of deep ocean temperature change from hydrographic sections and demonstrate this framework in an eddy-permitting ocean model. Biases in estimates from observations arise due to sparse spatial coverage (few sections in a basin), low frequency of occupations (typically 5-10years apart), mismatches between the time period of interest and span of occupations, and from seasonal biases relating to the practicalities of sampling during certain times of year. Between the years 1990 and 2010, the modeled global abyssal ocean biases are small, although regionally some biases (expressed as a heat flux into the 4,000- to 6,000-m layer) can be up to 0.05W/m(2). In this model, biases in the heat flux into the deep 2,000- to 4,000-m layer, due to either temporal or spatial sampling uncertainties, are typically much larger and can be over 0.1W/m(2) across an ocean. Overall, 82% of the warming trend deeper than 2,000m is captured by hydrographic section-style sampling in the model. At 2,000m, only half the model global warming trend is obtained from observational-style sampling, with large biases in the Atlantic, Southern, and Indian Oceans. Biases due to different sources of uncertainty can have opposing signs and differ in relative importance both regionally and with depth, revealing the importance of reducing temporal and spatial uncertainties in future deep ocean observing design.

Plain Language Summary In recent decades, deep (below 2,000m) ocean temperature trends have been measured when scientific research vessels repeat the same lines across an ocean basin. Repeats typically happen once or twice a decade, and there are only a few repeated lines across each basin. The sparsity of data in both space and time will result in errors in the multidecadal temperature trends calculated from this data. Here, we use a state-of-the-art ocean model to show how trends calculated from observational-style sampling compare to trends calculated using all model data. For the period 1990-2010, we estimate the error that may exist in observed deep ocean trend estimates. Overall, around 80% of the below 2,000-m warming trend was captured by observational-style sampling in the model, so deep ocean warming in recent decades may have been underestimated. However, our results are based on only one model simulation. The largest sources of sampling error are found in the Atlantic, Southern, and Indian Oceans. For each basin, we reveal whether limited sampling in time or space contributes most error to the temperature trend estimate, and therefore in which regions temperature trend estimates would benefit from additional deep ocean sampling.