What methods exist for remote profiling of oceanic columns?
There are a number of programs and instruments that sample the ocean autonomously. Examples of such programs are:


The ARGO program (http://www.argo.net/): Currently around 3000 floats are freely drifting in the ocean measuring temperature, salinity and in some cases velocity of the upper 1000-2000 meters of the ocean. The floats drift for around 10 days most commonly at 1000 or 2000 meters and then conduct a vertical profile to the surface where they transfer the data to a satellite. 
RAFOS floats (http://www.whoi.edu/instruments/viewInstrument.do?id=1061): They map the ocean currents using the SOFAR channel (a horizontal layer in the ocean where sound speed is minimum).
Gliders (http://www.ioos.noaa.gov/glider/): A type of autonomous underwater vehicle (AUV) that uses buoyancy to control its vertical position in the ocean. They sample along predetermined routes and can be equipped with instruments to measure temperature, salinity, turbidity, velocity...
Other AUVs: Most other AUVs use propellers powered by rechargeable batteries and are able to carry a lot more instruments, but are limited to shorter missions.


Measuring oceanographic interior conditions remotely is much more challenging. While satellites provide data for sea surface (or near-surface) parameters, such as temperature (e.g., MODIS), salinity (SMOS &amp; Aquarius), height (e.g., Jason 2) and color (SeaWiFS, MODIS), remote interior data are more challenging to acquire. 

Seismic oceanography is a recently developed technique that uses multichannel seismic reflection to characterize the ocean interior. It provides continuous mapping of the finer structure associated with the thermohaline (temperature and salinity) structure of the ocean. One of the best examples is Holbrook et al., 2003 Science paper (sciencemag.org/content/301/5634/821.full). You can find more information in: steveholbrook.com/research/seismic_oceanography and www.utm.csic.es/so