Measurement of total AC resistance (including radiation resistance) of a coil using LCR meter
I am measuring resistance of a coil underwater and I noticed a
  significant increase in resistance compared to the air surrounding. I
  wanted to confirm that the increase is due to the increase of
  radiation resistance.


Water conducts quite well and of course sea water conducts a lot better. What you are seeing is the effect of induced eddy currents (electrical) in the water. Literally, your coil creates a changing magnetic field and this induces an electric field in the water and the water acts as a resistor and electrical currents are produced.

It has nothing to do with radiation resistance - radiation resistance is a phenomena associated with the transmission of EM power through a medium. What you are seeing is a resistance due to near-field effects and eddy currents in the water.