What type of data is available for ocean depth and density? For instance, are there measurements of density near Greenland or Antarctica that could be compared to the central Pacific? It would be nice to have temperature and salinity measurements to go along with the density values. Also, how deep and how often are measurements made of density as a function of depth in the ocean?
There are several global products for temperature, salinity and pressure. The product that has been evolving for the longest is likely the World Ocean Database and World Ocean Atlas Series (https://www.nodc.noaa.gov/OC5/indprod.html) and their latest product WOA13 is very high quality (https://www.nodc.noaa.gov/OC5/woa13/). They also have the entire database of used observations.
A way to get a global database and also a way to visualize it and extract information is HydroBase.
Another fabulous product that includes global information available monthly for the period 1900 to the present is provided by the Met Office Haddley Centre. Their latest product is excellent.
If you are looking for model results, one option is to look at the global operational solutions as part of the GODAE initiative. A list of products is here. Their model products include data assimilation, which helps the model from going to far from reality. The one I am most familiar with is HYCOM, which provides global data assimilative products at 1/12 degree resolution.
You can find modeling data on the thermocline depth at the Global Change Master Directory at NASA. Here is a link that allows you to download the data: http://gcmd.nasa.gov/records/GCMD_IGOSS_NMC_PACMON_THERMOCLINE.html
This data is from hindcast results derived from a model based ocean analysis system. Observed surface and subsurface ocean temperatures as well as satellite altimetry sea-level data from TOPEX/POSEIDON are assimilated into a Pacific basin ocean general circulation model. The model is forced with weekly mean NCEP operational atmospheric analyses of surface winds and heat fluxes.