VENM: An Algorithm to Accurately Calculate Neutral Slopes and Gradients.

Mesoscale eddies stir along the neutral plane, and the resulting neutral diffusion is a fundamental aspect of subgrid-scale tracer transport in ocean models. Calculating neutral diffusion traditionally involves calculating neutral slopes and three-dimensional tracer gradients. The calculation of the neutral slope traditionally occurs by computing the ratio of the horizontal to vertical locally referenced potential density derivative. However, this approach is problematic in regions of weak vertical stratification, prompting the use of a variety of ad hoc regularization methods that can lead to rather nonphysical dependencies for the resulting neutral tracer gradients. Here we use a VErtical Non-local Method "VENM," a search algorithm that requires no ad hoc regularization and significantly improves the numerical accuracy of calculating neutral slopes, neutral tracer gradients, and associated neutral diffusive fluxes. We compare and contrast VENM against a more traditional method, using an independent objective neutrality condition combined with estimates of spurious diffusion, heat transport, and water mass transformation rates. VENM is more accurate, both physically and numerically, and should form the basis for future efforts involving neutral diffusion calculations from observations and possibly numerical model simulations.

Improved estimates of upper-ocean warming and multi-decadal sea-level rise.

Changes in the climate system's energy budget are predominantly revealed in ocean temperatures and the associated thermal expansion contribution to sea-level rise. Climate models, however, do not reproduce the large decadal variability in globally averaged ocean heat content inferred from the sparse observational database, even when volcanic and other variable climate forcings are included. The sum of the observed contributions has also not adequately explained the overall multi-decadal rise. Here we report improved estimates of near-global ocean heat content and thermal expansion for the upper 300 m and 700 m of the ocean for 1950-2003, using statistical techniques that allow for sparse data coverage and applying recent corrections to reduce systematic biases in the most common ocean temperature observations. Our ocean warming and thermal expansion trends for 1961-2003 are about 50 per cent larger than earlier estimates but about 40 per cent smaller for 1993-2003, which is consistent with the recognition that previously estimated rates for the 1990s had a positive bias as a result of instrumental errors. On average, the decadal variability of the climate models with volcanic forcing now agrees approximately with the observations, but the modelled multi-decadal trends are smaller than observed. We add our observational estimate of upper-ocean thermal expansion to other contributions to sea-level rise and find that the sum of contributions from 1961 to 2003 is about 1.5 +/- 0.4 mm yr(-1), in good agreement with our updated estimate of near-global mean sea-level rise (using techniques established in earlier studies) of 1.6 +/- 0.2 mm yr(-1).